**NCERT Exemplar Problems Class 7 Maths – Comparing Quantities**

**Question 1: **20% of 700 m is

(a) 560 m (b) 70 m (c)210 m (d)140 m

**Solution :**

(d) We have, 20% of 700 m = x 700 = 20 x 7 = 140 m

Hence, 20% of 700 m is 140 m.

**Question 2: **Gayatri’s income is Rs 160000 per year. She pays 15% of this as house rent and 10% of the remainder on her child’s education. The money left with her is

(a) Rs 136000 (b) Rs 120000 (c) Rs 122400 (d) Rs 14000

**Solution :**

(c) Income of Gayatri = ? 160000 [given]

Money paid as house rent = 15% of 160000 = x 160000 = Rs 24000

Remaining amount = 160000 – 24000 = Rs 136000

Money spent on child’s education = 10%of 136000 = x 136000 = Rs 13600

Money left with her = 136000 -13600= Rs 122400

**Question 3:**

The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money saved by her is

(a) 20% (b) 25% (c) 40% (d) 80%

**Solution :**

(a) Given, ratio of income to savings = 4:1

**Question 4: **0.07 is equal to

(a) 70% (b) 7%

(c) 0.7% (d) 0.07%

**Solution :**

(b) We have, 0.07

In percentage, 0.07 =x100%=7%

**Note:**To convert any number into per cent, we multiply that number by 100 along with the symbol ‘%’

**Question 5: **In a scout camp, 40% of the scouts were from Gujarat state and 20% of these were from Ahmedabad. The percentage of scouts in the camp from Ahmedabad is

(a) 25% (b) 32.5%

(c) 8% (d) 50%

**Solution :**

(c) Let the scouts in scout camp = 100

**Question 6: **What per cent of Rs 4500 is Rs 9000?

(a) 200% (b) 1/2%

(c) 2% (d) 50%

**Solution :**

**Question 7: **5.2 is equal to

(a) 52% (b) 5.2%

(c) 520% (d) 0.52%

**Solution :**

(c) We have, 5.2

In percentage, x 100% = 520%

**Question 8: **The ratio 3 : 8 is equal to

(a) 3.75% (b) 37.5% (c) 0.375% (d) 267%

**Solution :**

(b) Given, ratio =3:8

In percentage, x 100% = 37.5%

**Question 9: **225% is equal to

(a) 9 : 4 (b) 4 : 9 (c) 3 : 2 (d) 2 : 3

**Solution :**

(a) We have, 225%

For fraction, 225 x

∴ Required ratio = 9:4

**Note:**The sign of percentage (%) is removed dividing the number by 100.

**Question 10: **A bicycle is purchased for Rs 1800 and is sold at a profit of 12%. Its selling price is

(a) Rs 1584 (b) Rs 2016 (c) Rs 1788 (d) Rs 1812

**Solution :**

(b) Given, cost price of bicycle = ? 1800 and profit =12%

As we know,

**Question 11: **A cricket bat was purchased for Rs 800 and was sold for Rs 1600. Then, profit earned is

(a) 100% (b) 64% (c) 50% (d) 60%

**Solution :**

**Question 12: **A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the buffalo at a loss of 5% but made a profit of 10% on the cow. The net result of the transaction is

(a) loss of Rs 200 (b) profit of Rs 400

(c) loss of Rs 400 (d) profit of Rs 200

**Solution :**

**Question 13: **If Mohan’s income is 25% more than Raman’s income, then Raman’s income is less than Mohan’s income by

(a) 25% (b) 80%

(c) 20% (d) 75%

**Solution :**

(c) Let the Raman’s income be x. it is given that Mohan’s income is 25% more than

Raman’s income.

**Question 14: **The interest on t 30000 for 3 yr at the rate of 15% per annum is

(a) 7 4500 (b) 7 9000 (c) 7 18000 (d) 7 13500

**Solution :**

**Question 15: **Amount received on Rs 3000 for 2 yr at the rate of 11% per annum is

(a) Rs 2340 (b) Rs 3660 (c) Rs 4320 (d) Rs 3330

**Solution :**

**Question 16: **Interest on Rs 12000 for 1 month at the rate of 10% per annum is

(a) Rs 1200 (b) Rs 600 (c) Rs 100 (d) Rs 12100

**Solution :**

**Question 17: **Rajni and Mohini deposited Rs 3000 and Rs 4000 in a company at the rate of 10% per annum for 3 yr and yr, respectively. The difference of the amounts received by them will be

(a) Rs 100 (b) Rs 1000 (c) Rs 900 (d) Rs 1100

**Solution :**

**Question 18: **If 90% of x is 315 km, then the value of x is

(a) 325 km (b) 350 km (c) 405 km (d) 340 km

**Solution :**

**Question 19: **On selling an article for Rs 329, a dealer lost 6%. The cost price of the article is

(a) Rs 310.37 (b) Rs 348.74 (c) Rs 335 (d) Rs 350

**Solution :**

**Question 20:**

**Solution :**

**Question 21: **The sum which will earn a simple interest of Rs 126 in 2 yr at 14% per annum, is

(a) Rs 394 (b) Rs 395 (c) Rs 450 (d) Rs 540

**Solution :**

**Question 22: **The per cent that represents the unshaded region in the figure, is

**Solution :**

**Question 23: **The per cent that represents the shaded region in the figure, is

**Solution :**

**Fill in the Blanks**

In questions 24 to 59, fill in the blanks to make the statements true.

**Question 24: **2

**:**3=_____%

**Solution :**

Given ratio = 2:3

In percentage=2/3 x 100%=%

**Question 25: ** % =___:___

**Solution :**

**Question 26: **30% of Rs 360 = ________

**Solution :**

We have, 30% of Rs 360 = x 360 = Rs 108

**Question 27: **120% of 50 km =___________

**Solution :**

We have, 120% of 50 km = x 50 km = 60 km

**Question 28: **2.5 =_____%

**Solution :**

We have, 2.5

In percentage, 2.5 x 100% = 250%

**Question 29: **8/5=____%

**Solution :**

We have, 8/5

In percentage, 8/5 x 100% = 160%

**Question 30: **A_____with its denominator 100 is called a per cent.

**Solution :**

A fraction with its denominator 100 is called a per cent.

**Question 31: **15 kg is____% of 50 kg.

**Solution :**

**Question 32: **Weight of Nikhil increased from 60 kg to 66 kg. Then, the increase in weight is_____%

**Solution :**

We have, initial weight of Nikhil = 60 kg

After increase in weight, weight became =66 kg ‘ Increase in weight = 66 – 60 = 6 kg

∴ Increase percentage of weight

x100%= x100%= %=10%

So, the number of students present on that day, was 46.

**Question 33: **In a class of 50 students 8% were absent on one day. The number of students present on that day, was______.

**Solution :**

We have, total number of students =50 Absent on one day = 8%

Percentage of present students on that day = 100-8 = 92%

∴ Number of students present on that day = 92% of 50 = x 50 = = 46

So, the number of students present on that day, was 46.

**Question 34: **Savitri obtained 440 marks out of 500 in an examination. She secured _____% marks in the examination.

**Solution :**

Marks obtained by Savitri out of 500 = 440

Percentage of marks obtained = x 100% = 88%

Hence, Savitri secured 88% marks in the examination.

**Question 35: **Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of the deposit. Now, the balance in her account is_____.

**Solution :**

Total deposit=Rs 1500

Amount withdrawn = 40% of Rs 1500 = x 1500 = Rs 600

∴ Balance in the account = 1500 – 600 = Rs 900

**Question 36: **____ is 50% more than 60.

**Solution :**

Let number be x. It is given that x is 50% more than 60.

Therefore, x = 60 + 50% of 60 = 60 + x 60 = 60 + 30 = 90

**Question 37: **John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat is___.

**Solution :**

Given, SP of bat = Rs 75 and loss = Rs 8

We know that, CP = SP + Loss = 75 + 8 = Rs 83

Hence, cost price of the bat is Rs 83.

**Question 38: **If the price of sugar is decreased by 20%, then the new price of 3kg sugar originally costing Rs 120, will be______.

**Solution :**

Original price of 3 kg sugar = Rs 120

Given that, price of sugar is decreased by 20%.

So, new price of sugar = Original price – 20% of original price

= 120 – 20% of 120

= 120- x 120= 120-24=Rs 96 100

**Question 39: **Mohini bought a cow for Rs 9000 and Sold it at a loss of Rs 900. The selling price of the cow is_______.

**Solution :**

Given, CP of cow=Rs 9000 and loss = Rs 900

We know that, SP = CP – Loss = 9000 – 900=Rs 8100

Hence, the selling price of the cow is Rs 8100.

**Question 40: **Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of______% in the transaction.

**Solution :**

**Question 41: **Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her____ % is___%.

**Solution :**

**Question 42: **Nasim bought a pen for Rs 60 and sold it for Rs 54. His_____________ % is

**Solution :**

**Question 43: **Aahuti purchased a house for Rs 5059700 and spent Rs 40300 on its repairing. To make a profit of 5%, she should sell the house for Rs_______ .

**Solution :**

**Question 44: **If 20 lemons are bought for Rs 10 and sold at 5 for three rupees, then______in the transaction is_____%.

**Solution :**

**Question 45: **Narain bought 120 oranges at Rs 4 each. He sold 60% of the oranges at Rs 5 each and the remaining at Rs 3.50 each. His_____is_____%.

**Solution :**

**Question 46: **A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of the apples were found to be rotten. If he sells the remaining apples at Rs 60 per kg, then his_____is_____% .

**Solution :**

**Question 47: **Interest on Rs 3000 at 10% per annum for a period of 3 yr is______ .

**Solution :**

**Question 48: **Amount obtained by depositing Rs 20000 at 8% per annum for six months, is_____.

**Solution :**

**Question 49: **Interest on Rs 12500 at 18% per annum for a period of 2 yr and 4 months is______.

**Solution :**

**Question 50: **25 mL is_____% of 5 L.

**Solution :**

**Question 51: **If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then,_____% of A is equal to C.

**Solution :**

**Question 52: **Interest = , where T is_____,R% is____ and P is____.

**Solution :**

Here, T is

**time period**, R% is

**rate of interest**and P is

**Principal.**

**Question 53: **The difference of interests for 2 yr and 3 yr on a sum of Rs 2100 at 8% per annum is_______.

**Solution :**

**Question 54: **To convert a fraction into a per cent, we______ it by 100.

To convert a fraction into a per cent, we multiply it by 100.

**Solution :**

**Question 55: **To convert a decimal into a per cent, we shift the decimal point two places to the_____.

**Solution :**

To convert a decimal into a per cent, we shift the decimal point into places to the right.

**Question 56:**

The_____of interests on a sum of Rs 2000 at the rate of 6% per annum for yr and 2 yr is Rs 420.

**Solution :**

**Question 57: **When converted into percentage, the value of 6.5 is______than 100%.

**Solution :**

We have, 6.5

In percentage, 6.5 x 100% = 650%

Hence, when converted into percentage, the value of 6.5 is more than 100%.

**In questions 68 and 59, copy each number line. Fill in the blanks, so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.**

**Question 58:**

**Solution :**

**Question 59:**

**Solution :**

**True/False**

In questions 60 to 79, state whether the statements are True or False.

**Question 60:**

**Solution :**

**Question 61: **When an improper fraction is converted into percentage, then the answer can also be less than 100.

**Solution :**

**False**

Consider, an improper fraction = (N > D)

In percentage, x 100% = 240%

Hence, when an improper fraction is converted into percentage, then the answer is always greater than 100.

**Question 62: **8 h is 50% of 4 days.

**Solution :**

**False**

Let 8 h be x% of 4 days.

**Question 63: **The interest on Rs 350 at 5% per annum for 73 days is Rs 35.

**Solution :**

**False**

**Question 64: **The simple interest on a sum of Rs P for T yr at R% per annum is given by the formula

Simple Interest=

**Solution :**

**True**

SI =

We can also write it as,SI = [since, multiplication is commutative]

**Question 65: **75% = 4/3

**Solution :**

**False**

**Question 66: **12% of 120 is 100.

**Solution :**

**False**

**Question 67: **If Ankita obtains 336 marks out of 600, then percentage of marks obtained by her is 33.6%.

**Solution :**

**False**

Marks obtained by Ankita out of 600 = 336

Percentage, marks = x 100% = 56%

Hence, Ankita got 56% marks.

**Question 68: **0.018 is equivalent to 8%.

**Solution :**

**False**

Given, decimal = 0.018

In percentage, 0.018 x 100= 1.8%

Hence, 0.018 is equivalent to 1.8%

**Question 69: **50% of Rs 50 is Rs 25.

**Solution :**

**True**

Since, 50% of Rs 50 = x 50= Rs 25

Hence, 50% of Rs 50 is Rs 25.

**Question 70: **250 cm is 4% of 1 km.

**Solution :**

**Question 71: **Out of 600 students of a school, 126 go for a picnic. The percentage of students that did not go for the picnic, is 75.

**Solution :**

**False**

Total students =600 Students went for picnic = 126

∴ Students did not go for picnic = 600 -126= 474

In percentage, x 100% = 79%

Hence, 79% of students did not go for picnic.

**Question 72: **By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost price of the book is Rs 60.

**Solution :**

**Question 73: **If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price of the chair is Rs 2010.

**Solution :**

**Question 74: **If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of profit is 10%.

**Solution :**

**Question 75: **Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of 10%, she should have sold the watch for Rs 3300.

**Solution :**

**Question 76: **Interest on Rs 1200 for yr at the rate of 15% per annum is Rs 180.

**Solution :**

**Question 77: **Amount received after depositing Rs 800 a period of 3 yr at the rate of 12% per annum is Rs 896.

**Solution :**

**Question 78: **Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 3 and 5 yr, respectively. The difference in the interests paid by them is Rs 150.

**Solution :**

**Question 79: **A vendor purchased 720 lemons at Rs 120 per hundred. 10% of the lemons were found rotten, which he sold at Rs 50 per hundred. If he sells the remaining lemons at Rs 125 per hundred, then his profit will be 16%.

**Solution :**

**Question 80: **Find the value of x, if

(a) 8% of Rs x is ? 100.

(b) 32% of x kg is 400 kg.

(c) 35% of Rs x is ?280.

(d) 45% of marks x is 405.

**Solution :**

**Question 81: **Imagine that, a 10 x 10 grid has value 300 and that this value is divided evenly among the small squares. In other words, each small square is worth 3. Use a new grid for each part of this problem and label each grid “Value : 300”.

(a) Shade 25% of the grid. What is 25% of 300? Compare the two answers.

(b) What is the value of 25 squares?

(c) Shade 17% of the grid. What is 17% of 300? Compare the two answers.

(d) What is the value of 1/10 of the grid?

**Solution :**

**Question 82: **Express as a per cent.

**Solution :**

**Question 83: **Express as a per cent.

**Solution :**

We have,

In percentage, x 100%=%

**Question 84: **Express as a per cent.

**Solution :**

We have,

In percentage, x 100%= 1%

**Question 85: **Express 80% as a fraction in its lowest form.

**Solution :**

**Question 86: **Express 33 % as a ratio in the lowest form.

**Solution :**

**Question 87: **Express 16 % as a ratio in the lowest form.

**Solution :**

**Question 88: **Express 150% as a ratio in the lowest form.

**Solution :**

**Question 89: **Sachin and Sanjana are calculating 23% of 800.

Now, calculate 52% of 700 using both the ways described above. Which way do you find easier?

**Solution :**

**Question 90: **Write 0.089 as a per cent.

**Solution :**

We have, 0.089

In percentage, 0.089 x 100% = 8.9% [to convert in per cent, multiply by 100]

**Question 91: **Write 1.56 as a per cent.

**Solution :**

We have, 1.56

In percentage, 1.56 x 100%= 156%

**Question 92: **What is 15% of 20?

**Solution :**

We have, 15% of 20

= x 20 = 3

**Question 93: **What is 800% of 800?

**Solution :**

We have, 800% of 800

= x 800 = 6400

**Question 94: **What is 100% of 500?

**Solution :**

We have, 100% of 500

= x 500= 500

**Question 95: **What per cent of 1 h is 30 min?

**Solution :**

**Question 96: **What per cent of 1 day is 1 min?

**Solution :**

**Question 97: **What per cent of 1 km is 1000 m?

**Solution :**

**Question 98: **Find out 8% of 25 kg.

**Solution :**

**Question 99: **What per cent of Rs 80 is Rs 100?

**Solution :**

**Question 100: **45% of the population of a town are men and 40% are women. What is the percentage of children?

**Solution :**

We have,

Percentage of men in town = 45%

Percentage of women in town = 40%

So, percentage of children in town = 100 – 45 – 40= 100 – 85= 15%

Hence, 15% of the population of a town are children.

**Question 101: **The strength of a school is 2000. If 40% of the students are girls, then how many boys are there in the school?

**Solution :**

As per the given information in the question,

The strength of school = 2000 Percentage of girls in school = 40%

Percentage of boys in school = 100- 40 = 60%

Number of boys in school = 60% of 2000 = x 2000= 60 x 20 = 1200

Hence, number of boys in school is 1200.

**Question 102: **Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in kg of chalk.

**Solution :**

We have,

Percentage of calcium in chalk = 10%

Percentage of carbon in chalk = 3%

Percentage of oxygen in chalk = 12%

**Question 103: **800 kg of mortar consists of 55% sand, 33% cement and rest lime. What is the mass of lime in mortar?

**Solution :**

We have,

Percentage of sand in mortar = 55%

Percentage of cement in mortar = 33%

So, percentage of lime in mortar = 100 – 55 – 33 = 100 – 88 = 12%

∴ Weight of mortar = 800 kg

∴ Mass of lime in mortar = 12% of 800 kg = x 800 = 12 x 8 = 96 kg

Hence, weight of lime in mortar is 96 kg.

**Question 104: **In a furniture shop, 24 tables were bought at the rate of Rs 450 per table. The shopkeeper sold 16 of them at the rate of Rs 600 per table and the remaining at the rate of 400 per table. Find her gain or loss per cent.

**Solution :**

**Question 105: **Medha deposited 20% of her money in a bank. After spending 20% of the remainder, she has Rs 4800 left with her. How much did she originally have?

**Solution :**

**Question 106: **The cost of a flower vase got increased by 12%. If the current cost is Rs 896, what was its original cost?

**Solution :**

**Question 107: **Radhika borrowed Rs 12000 from her friends. Out of which Rs 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 yr?

**Solution :**

**Question 108: **A man travelled 60 km by car and 240 km by train. Find what per cent of total journey did he travel by car and what per cent by train?

**Solution :**

Distance covered by car = 60 km

Distance covered by train = 240 km

∴ Total journey = 60 + 240= 300 km

**Question 109: **By selling a chair for Rs 1440, a shopkeeper loses 10%. At what price, did he buy it?

**Solution :**

**Question 110: **Dhruvika invested money for a period from May 2006 to April 2008 at the rate of 12% per annum. If interest received by her is Rs 1620, then find the money invested.

**Solution :**

**Question 111: **A person wanted to sell a scooter at a loss of 25%. But at the last moment, he changed his mind and sold the scooter at a loss of 20%. If the difference in the two SP’s is Rs 4000, then find the CP of the scooter.

**Solution :**

**Question 112: **The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women. Find the ratio of the number of literate women to the total population.

**Solution :**

**Question 113: **In an entertainment programme, 250 tickets of Rs 400 and 500 tickets of Rs 100 were sold. If the entertainment tax is 40% on ticket of Rs 400 and 20% on ticket of Rs 100, then find how much entertainment tax was collected from the programme?

**Solution :**

It is given that, 250 tickets of Rs 400 were sold, Therefore, total amount received by selling these tickets = 250 x 400= Rs 100000

Similarly, amount received by selling 500 tickets of Rs 100 = 500 x 100= Rs 50000

It is also given that, 40% and 20% of entertainment tax is on Rs 400 and Rs 100 tickets, respectively.

So, total entertainment tax collected

**Question 114:**

Bhavya earns Rs 50000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she lias to spent 20% more. Find her new savings.

**Solution :**

**Question 115: **In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first paper and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70% marks?

**Solution :**

**Question 116: **

**Health Application**

A doctor reports blood pressure in millimetres of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.

Manohar is a healthy 37 yr old man whose blood pressure is in the normal category.

(a) Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.

(b) If Manohar’s systolic blood pressure is 102 mm Hg, then use the ratio from part (a) to predict his diastolic blood pressure.

(c) Calculate ratio of average systolic to average diastolic blood pressures in the prehypertension category.

**Solution :**

**Question 117: **(a) Science Application

The king cobra can reach a Length of 558 cm. This is only about 60% of the length of the largest reticulated python. Find the length of the largest reticulated python.

(b) Physical Science Application

Unequal masses will not balance on a fulcrum, if they are at equal distance from it, one side will go up and the other side will go down.

Unequal masses will balance when the following proportion is true.

The child on the left and child on the right are balanced. What is the mass of the child on the right?

(c) Life Science Application

A DNA model was built using the scale 2 cm : 0.0000001 mm. If the model of the DNA chain is 17 cm long, what is the length of the actual chain?

**Solution :**

**Question 118: **Language Application

Given below are few mathematical terms.

Find

(a) The ratio of consonants to vowels in each of the terms.

(b) The percentage of consonants in each of the terms.

**Solution :**

**Question 119: **What’s the Error? An analysis showed that 0.06% of the T-shirts made by one company were defective. A student says this is 6 out of every 100. What is the student’s error?

**Solution :**

**Question 120: **What’s the Error? A student said that the ratios and were proportional. What error did the student make?

**Solution :**

Hence, the ratios are not proportional. To make a ratio proportional to another ratio, we just simply multiply both numerator and denominator by same number.

In our given case, student had multiply numerator by 3 and denominator by 4, which is incorrect.

**Question 121: **What’s the Error? A clothing store charges Rs 1024 for 4 T-shirts. A student says that the unit price is Rs 25.6 per T-shirt. What is the error? What is the correct unit price?

**Solution :**

**Question 122: **A tea merchant blends two varieties of tea in the ratio of 5:4. The cost of first variety is Rs 200 per kg and that of second variety is Rs 300 per kg. If he sells the blended tea at the rate of Rs 275 per kg, then find out the percentage of his profit or loss.

**Solution :**

Given, ratio of blended two varieties of tea (green tea : lemon tea) = 5:4

Cost of green tea = Rs 200 per kg

Cost of lemon tea = Rs 300 per kg

SP of blended tea = Rs 275 per kg

According to the ratio,

Let green tea be 5x kg and lemon tea be 4x kg.

Then, cost of green tea = 5x x 200 = Rs 1000x

Cost of lemon tea = 4x x 300 = Rs 1200x

Total CP = 1000x + 1200x = Rs 2200x

Total quantity = 4x + 5x = 9x kg So,

**Question 123: **A piece of cloth 5 m long shrinks 10% on washing. How long will the cloth be after washing?

**Solution :**

**Question 124: **Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?

**Solution :**

**Question 125: **A memorial trust donates Rs 500000 to a school, the interest on which is to be used for awarding 3 scholarships to students obtaining first three positions in the school examination every year. If the donation earns an interest of 12% per annum and the values of the second and third scholarships are Rs 20000 and Rs 15000 respectively, then find out the value of the first scholarship.

**Solution :**

**Question 126: **Ambika got 99% marks in Mathematics, 76% marks in Hindi, 61% in English, 84% in Science and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.

**Solution :**

**Question 127: **What sum of money lent out at 16% per annum simple interest, so that it would produce Rs 9600 as interest in 2 yr?

**Solution :**

**Question 128: **Harish bought a gas-chullah for Rs 900 and later sold it to Archana at a profit of 5%. Archana used it for a period of two years and later sold it to Babita at a loss of 20%. For how much did Babita get it?

**Solution :**

It is given that, Harish bought the chullah for Rs 900 and sold it to Archana at a profit of 5%.

**Question 129: **Match each of the entries in Column I with the appropriate entries in Column II

**Solution :**

**Question 130: **In a debate competition, the judges decide that 20% of the total marks would be given for accent and presentation. 60% of the rest are reserved for the subject matter and the rest are for rebuttal. If this means 8 marks for rebuttal, then find the total marks.

**Solution :**

**Question 131: **Divide Rs 10000 in two parts, so that the simple interest on the first part for 4 yr at 12% per annum may be equal to the simple interest on the second part for 4.5 yr at 16% per annum.

**Solution :**

Given, money= Rs 10000

Now, we have divide Rs 10000 in two parts such that SI on first part for 4 yr at 12%

per annum may be equal to the SI on second part for 4.5 yr at 16%.

Let first part = 7 x

Then, second part = Rs (10000 – x)

**Question 132: **Rs 9000 becomes Rs 18000 at simple interest in 8 yr. Find the rate per cent per annum.

**Solution :**

**Question 133: **In how many years, will the simple interest on a certain sum be 4.05 times the principal at 13.5% per annum?

**Solution :**

**Question 134: **The simple interest on a certain sum for 8 yr at 12% per annum is Rs 3120 more than the simple interest on the same sum for 5 yr at 14% per annum. Find the sum.

**Solution :**

**Question 135: **The simple interest on a certain sum for 2.5 yr at 12% per annum is Rs 300 less than the simple interest on the same sum for 4.5 yr at 8% per annum. Find the sum.

**Solution :**

**Question 136: **Designing a Healthy Diet

When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.

- Calculate your ideal weight as per your height from the table given at the end of this question.
- An active child should eat around 55.11 calories for each kilogram desired weight.
- 55% of calories should come from carbohydrates. There are 4 calories in each gram of carbohydrates.
- 15% of your calories should come from proteins. There are 4 calories in each gram of proteins.
- 30% of your calories may come from fats. There are 9 calories in each gram of fats.

Following is an example to design your own healthy diet.

**Solution :**

**Question 137: **150 students are studying English, Maths or both. 62% of students study English and 68% are studying Maths. How many students are studying both?

**Solution :**

**Question 138: **

**Earth Science**

The table lists the world’s 10 largest deserts.

(a) What are the mean, median and mode of the areas listed?

(b) How many times the size of the Gobi Desert is the Namib Desert?

(c) What percentage of the deserts listed are in Asia?

(d) What percentage of the total area of the deserts listed is in Asia?

**Solution :**

**Question 139: **

**Geography Application**

Earth’s total land is about 148428950 km

^{2}. The land area of Asia is about 30% of this total. What is the approximate land area of Asia to the nearest square kilometre?

**Solution :**

**Question 140: **The pieces of Tangrams have been rearranged to make the given shape.

By observing the given shape, answer the following questions.

(a) What percentage of total has been coloured?

(i) Red (R) =_______

(ii) Blue (B) =_______

(iii) Green (G) =_______

(b) Check that the sum of all the percentages calculated above should be 100.

(c) If we rearrange the same pieces to form some other shape, will the percentage of colours change?

**Solution :**