NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 7: Comparing Quantities

Problems and Solutions

Find the value of x if

(i) 8% of ₹ x is ₹ 100

(ii) 32% of x kg is 400 kg

(iii) 35% of ₹ x is ₹ 280

(iv) 45% of marks x is 405

Imagine that a 10 × 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?

Express 1/6 as a per cent.

Express 9/40 as a per cent.

Express 1/100 as a per cent.

Express 80% as fraction in its lowest term.

Express 33 1/3% as a ratio in the lowest term.

Express 16 2/3% as a ratio in the lowest form.

Express 150% as a ratio in the lowest form.

Sachin and Sanjana are calculating 23% of 800.

Write 0.089 as a per cent.

Write 1.56 as a per cent.

What is 15% of 20?

What is 800% of 800?

What is 100% of 500?

What per cent of 1 hour is 30 minutes?

What per cent of 1 day is 1 minute?

What per cent of 1 km is 1000 metres?

Find out 8% of 25 kg.

What percent of ₹ 80 is ₹ 100?

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

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

Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in 2 1/2 kg of chalk.

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

In a furniture shop, 24 tables were bought at the rate of ₹ 450 per table. The shopkeeper sold 16 of them at the rate of ₹ 600 per table and the remaining at the rate of 400 per table. Find her gain or loss percent.

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

The cost of a flower vase got increased by 12%. If the current cost is ₹ 896, what was its original cost?

Radhika borrowed ₹ 12000 from her friends. Out of which ₹ 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 years?

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?

By selling a chair for ₹ 1440, a shopkeeper loses 10%. At what price did he buy it?

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

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 ₹ 4000, then find the CP of the scooter.

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.

In an entertainment programme, 250 tickets of ₹ 400 and 500 tickets of ₹ 100 were sold. If the entertainment tax is 40% on ticket of ₹ 400 and 20% on ticket of ₹ 100, find how much entertainment tax was collected from the programme.

Bhavya earns ₹ 50,000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she has to spend 20% more. Find her new savings.

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

Health Application: A doctor reports blood pressure... Refer to the table of blood pressure ranges for adults. Manohar 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, use the ratio from part (a) to predict his diastolic blood pressure.

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

(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... If mass1 = 24 kg at 3 m and length2 = 2 m, find mass of child on 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?

Language Application: Given below are few Mathematical terms: Hypotenuse, Congruence, Perpendicular, Transversal, Correspondence.

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

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

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?

What's the Error? A student said that the ratios 3/4 and 9/16 were proportional. What error did the student make?

What's the Error? A clothing store charges ₹ 1024 for 4 T-shirts. A student says that the unit price is ₹ 25.6 per T-shirt. What is the error? What is the correct unit price?

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

A piece of cloth 5 m long shrinks 10 per cent on washing. How long will the cloth be after washing?

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

A memorial trust donates ₹ 5,00,000 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 ₹ 20,000 and ₹ 15,000 respectively, find out the value of the first scholarship.

Ambika got 99 per cent marks in Mathematics, 76 per cent marks in Hindi, 61 per cent in English, 84 per cent 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.

What sum of money lent out at 16 per cent per annum simple interest would produce ₹ 9600 as interest in 2 years?

Harish bought a gas-chullah for ₹ 900 and later sold it to Archana at a profit of 5 per cent. Archana used it for two years and later sold it to Babita at a loss of 20 per cent. For how much did Babita get it?

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

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

Divide ₹ 10000 in two parts so that the simple interest on the first part for 4 years at 12% per annum equals the simple interest on the second part for 4.5 years at 16% per annum.

₹ 9000 becomes ₹ 18000 at simple interest in 8 years. Find the rate of interest per annum.

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

The simple interest on a certain sum for 8 years at 12% per annum is ₹ 3120 more than the simple interest on the same sum for 5 years at 14% per annum. Find the sum.

The simple interest on a certain sum for 2.5 years at 12% per annum is ₹ 300 less than the simple interest on the same sum for 4.5 years at 8% per annum. Find the sum.

Designing a Healthy Diet: Answer the given questions.

150 students are studying English, Maths or both. 62% study English and 68% study Maths. How many are studying both?

Earth Science: Refer table of world’s largest deserts. Answer:

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

Geography Application: Earth’s total land = 148428950 km². Asia’s land = 30% of this. Find approximate land area of Asia.

Tangram: Find percentage of each color.