NCERT Exemplar solutions for Mathematics [English] Class 8 chapter 9 - Comparing Quantities [Latest edition]

Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities.

1. C > S
2. C = S
3. C < S

Then

Suppose a certain sum doubles in 2 years at r % rate of simple interest per annum or at R% rate of interest per annum compounded annually. We have ______.

The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is ______.

If marked price of an article is Rs 1,200 and the discount is 12% then the selling price of the article is ______.

If 90% of x is 315 km, then the value of x is ______.

To gain 25% after allowing a discount of 10%, the shopkeeper must mark the price of the article which costs him Rs 360 as ______.

If a % is the discount percent on a marked price x, then discount is ______.

Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half-yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is ______.

For calculation of interest compounded half yearly, keeping the principal same, which one of the following is true?

Shyama purchases a scooter costing Rs 36,450 and the rate of sales tax is 9%, then the total amount paid by her is ______.

The marked price of an article is Rs 80 and it is sold at Rs 76, then the discount rate is ______.

A bought a tape recorder for Rs 8,000 and sold it to B. B in turn sold it to C, each earning a profit of 20%. Which of the following is true?

Latika bought a teapot for Rs 120 and a set of cups for Rs 400. She sold teapot at a profit of 5% and cups at a loss of 5%. The amount received by her is ______.

A jacket was sold for Rs 1,120 after allowing a discount of 20%. The marked price of the jacket is ______.

A sum is taken for two years at 16% p.a. If interest is compounded after every three months, the number of times for which interest is charged in 2 years is ______.

The original price of a washing machine which was bought for Rs 13,500 inclusive of 8% VAT is ______.

Avinash bought an electric iron for Rs 900 and sold it at a gain of 10%. He sold another electric iron at 5% loss which was bought Rs 1200. On the transaction he has a ______.

A TV set was bought for Rs 26,250 including 5% VAT. The original price of the TV set is ______.

40% of [100 – 20% of 300] is equal to ______.

Radhika bought a car for Rs 2,50,000. Next year its price decreased by 10% and further next year it decreased by 12%. In the two years overall decrease percent in the price of the car is ______.

______ is a reduction on the marked price of the article.

Increase of a number from 150 to 162 is equal to increase of ______ per cent.

15% increase in price of an article, which is Rs 1,620, is the increase of Rs ______.

Discount = ______ – ______.

Discount = Discount % of ______.

______ is charged on the sale of an item by the government and is added to the bill amount.

Amount when interest is compounded annually is given by the formula ______.

Sales tax = tax % of ______.

The time period after which the interest is added each time to form a new principal is called the ______.

______ expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.

The discount on an item for sale is calculated on the ______.

When principal P is compounded semi-annually at r % per annum for t years, then amount ______.

Percentages are ______ to fractions with ______ equal to 100.

The marked price of an article when it is sold for Rs 880 after a discount of 12% is ______.

The compound interest on Rs 8,000 for one year at 16% p.a. compounded half yearly is ______, given that (1.08)² = 1.1664.

In the first year on an investment of Rs 6,00,000 the loss is 5% and in the second year the gain is 10%, the net result is ______.

If amount on the principal of Rs 6,000 is written as `6000 [1 + 5/100]^3` and compound interest payable half yearly, then rate of interest p.a. is ______ and time in years is ______.

By selling an article for Rs 1,12,000 a girl gains 40%. The cost price of the article was ______.

The loss per cent on selling 140 geometry boxes at the loss of S.P. of 10 geometry boxes is equal to ______.

The cost price of 10 tables is equal to the sale price of 5 tables. The profit per cent in this transaction is ______.

Abida bought 100 pens at the rate of Rs 3.50 per pen and pays a sales tax of 4%. The total amount paid by Abida is ______.

The cost of a tape-recorder is Rs 10,800 inclusive of sales tax charged at 8%. The price of the tape-recorder before sales tax was charged is ______.

2500 is greater than 500 by ______ %.

Four times a number is a ______ % increase in the number.

5% sales tax is charged on an article marked Rs 200 after allowing a discount of 5%, then the amount payable is ______.

To calculate the growth of a bacteria if the rate of growth is known, the formula for calculation of amount in compound interest can be used.

Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.

Discount is a reduction given on cost price of an article.

Compound interest is the interest calculated on the previous year’s amount.

C.P. = M.P. – Discount.

A man purchased a bicycle for Rs 1,040 and sold it for Rs 800. His gain per cent is 30%.

Three times a number is 200% increase in the number, then one-third of the same number is 200% decrease in the number.

Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.

The cost of a sewing machine is Rs 7,000. Its value depreciates at 8% p.a. Then the value of the machine after 2 years is Rs 5,924.80.

If the discount of Rs y is available on the marked price of Rs x, then the discount percent is `x/y xx 100%`.

Number of students appearing for class X CBSE examination increases from 91,422 in 1999 – 2000 to 11,6054 in 2008 – 09. Increase in the number of students appeared is approximately 27%.

Selling price of 9 articles is equal to the cost price of 15 articles. In this transaction there is profit of `66 2/3%`.

The compound interest on a sum of Rs P for T years at R% per annum compounded annually is given by the formula `P(1 + R/100)`.

In case of gain, S.P. = `((100 + "gain"%) xx "C.P.")/100`.

In case of loss, `C.P. = (100 xx S.P.)/(100 + Loss%)`

The value of a car, bought for Rs 4,40,000 depreciates each year by 10% of its value at the beginning of that year. So its value becomes Rs 3,08,000 after three years.

The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs 192.

The buying price of 5 kg of flour with the rate Rs 20 per kg, when 5% ST is added on the purchase is Rs 21.

The original price of a shampoo bottle bought for Rs 324 if 8% VAT is included in the price is Rs 300.

Sales tax is always calculated on the cost price of an item and is added to the value of the bill.

In a factory, women are 35% of all the workers, the rest of the workers being men. The number of men exceeds that of women by 252. Find the total number of workers in the factory.

Three bags contain 64.2 kg of sugar. The second bag contains `4/5` of the contents of the first and the third contains `45 1/2`% of what there is in the second bag. How much sugar is there in each bag?

Find the S.P. if M.P. = Rs 5450 and discount = 5%

Find the S.P. if M.P. = Rs 1300 and discount = 1.5%

Find the M.P. if S.P. = Rs 495 and discount = 1%

Find the M.P. if S.P. = Rs 9,250 and discount = `7 1/2%`

Find discount in per cent when M.P. = Rs 625 and S.P. = Rs 562.50

Find discount in per cent when M.P. = Rs 900 and S.P. = Rs 873

The marked price of an article is Rs 500. The shopkeeper gives a discount of 5% and still makes a profit of 25%. Find the cost price of the article.

In 2007 – 08, the number of students appeared for Class X examination was 1,05,332 and in 2008 – 09, the number was 1,16,054. If 88,151 students pass the examination in 2007 – 08 and 103804 students in 2008 – 09. What is the increase or decrease in pass % in Class X result?

A watch worth Rs 5400 is offered for sale at Rs 4,500. What per cent discount is offered during the sale?

In the year 2001, the number of malaria patients admitted in the hospitals of a state was 4,375. Every year this number decreases by 8%. Find the number of patients in 2003.

Jyotsana bought a product for Rs 3,155 including 4.5% sales tax. Find the price before tax was added.

An average urban Indian uses about 150 litres of water every day.

What per cent of water is used for bathing and sanitation together per day?

An average urban Indian uses about 150 litres of water every day.

How much less per cent of water is used for cooking in comparison to that used for bathing?

An average urban Indian uses about 150 litres of water every day.

What per cent of water is used for drinking, cooking and gardening together?

In 1975, the consumption of water for human use was about 3850 cu.km/year. It increased to about 6000 cu.km/year in the year 2000. Find the per cent increase in the consumption of water from 1975 to 2000. Also, find the annual per cent increase in consumption (assuming water consumption increases uniformly).

Harshna gave her car for service at service station on 27-05-2009 and was charged as follows:

1. 3.10 litres engine oil @ Rs 178.75 per litre and VAT @ 20%.
2. Rs 1,105.12 for all other services and VAT @ 12.5%.
3. Rs 2,095.80 as labour charges and service tax @10%.
4. 3% cess on service Tax.
   Find the bill amount.

Given the principal = Rs 40,000, rate of interest = 8% p.a. compounded annually. Find

1. Interest if period is one year.
2. Principal for 2nd year.
3. Interest for 2nd year.
4. Amount if period is 2 years.

In Delhi University, in the year 2009 – 10,49,000 seats were available for admission to various courses at graduation level. Out of these 28,200 seats were for the students of General Category while 7,400 seats were reserved for SC and 3,700 seats for ST. Find the percentage of seats available for students of General Category.

In Delhi University, in the year 2009 – 10,49,000 seats were available for admission to various courses at graduation level. Out of these 28,200 seats were for the students of General Category while 7,400 seats were reserved for SC and 3,700 seats for ST. Find the percentage of seats available for students of SC Category and ST Category taken together.

Prachi bought medicines from a medical store as prescribed by her doctor for Rs 36.40 including 4% VAT. Find the price before VAT was added.

Kritika ordered one pizza and one garlic bread from a pizza store and paid Rs 387 inclusive of taxes of Rs 43. Find the tax%.

Arunima bought household items whose marked price and discount % is as follows:

Find the total amount of the bill she has to pay.

Devangi’s phone subscription charges for the period 17-02-09 to 16-03-09 were as follows:

Find the final bill amount if 3% education cess was also charged on service tax.

If principal = Rs 1,00,000. rate of interest = 10% compounded half yearly. Find

1. Interest for 6 months.
2. Amount after 6 months.
3. Interest for next 6 months.
4. Amount after one year.

Babita bought 160 kg of mangoes at Rs 48 per kg. She sold 70% of the mangoes at Rs 70 per kg and the remaining mangoes at Rs 40 per kg. Find Babita’s gain or loss per cent on the whole dealing.

A shopkeeper was selling all his items at 25% discount. During the off season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt which was marked for Rs 1,200, how much did she pay for it?

Ayesha announced a festival discount of 25% on all the items in her mobile phone shop. Ramandeep bought a mobile phone for himself. He got a discount of Rs 1,960. What was the marked price of the mobile phone?

Find the difference between Compound Interest and Simple Interest on Rs 45,000 at 12% per annum for 5 years.

A new computer costs Rs 1,00,000. The depreciation of computers is very high as new models with better technological advantages are coming into the market. The depreciation is as high as 50% every year. How much will the cost of computer be after two years?

The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 6,31,680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago?

Lemons were bought at Rs 48 per dozen and sold at the rate of Rs 40 per 10. Find the gain or loss per cent.

If the price of petrol, diesel and LPG is slashed as follows:

Complete the above table.

What is the percentage increase or decrease in the number of seats won by A, B, C and D in the general elections of 2009 as compared to the results of 2004?

How much more percent seats were won by X as compared to Y in Assembly Election in the state based on the data given below.

Ashima sold two coolers for Rs 3,990 each. On selling one cooler she gained 5% and on selling the other she suffered a loss of 5%. Find her overall gain or loss % in whole transaction.

A lady buys some pencils for Rs 3 and an equal number for Rs 6. She sells them for Rs 7. Find her gain or loss%.

On selling a chair for Rs 736, a shopkeeper suffers a loss of 8%. At what price should he sell it so as to gain 8%?

A dining table is purchased for Rs 3,200 and sold at a gain of 6%. If a customer pays sales tax at the rate of 5%. How much does the customer pay in all for the table?

Achal bought a second-hand car for Rs 2,25,000 and spend Rs 25,000 for repairing. If he sold it for Rs 3,25,000, what is his profit per cent?

A lady bought an air-conditioner for Rs 15,200 and spent Rs 300 and Rs 500 on its transportation and repair respectively. At what price should she sell it to make a gain of 15%?

What price should a shopkeeper mark on an article that costs him Rs 600 to gain 20%, after allowing a discount of 10%

Brinda purchased 18 coats at the rate of Rs 1,500 each and sold them at a profit of 6%. If customer is to pay sales tax at the rate of 4%, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?

Rahim borrowed Rs 10,24,000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.

The following items are purchased from showroom:

T-Shirt worth Rs 1200.

Jeans worth Rs 1000.

2 Skirts worth Rs 1350 each.

What will these items cost to Shikha if the sales tax is 7%?

The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)

Which can be measured more accurately : the total amount of fat in cream of tomato soup or the total amount of fat in sweet corn soup? Explain.

The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)

One serving of cream of tomato soup contains 29% of the recommended daily value of sodium for a 2000 calorie diet. What is the recommended daily value of sodium in milligrams? Express the answer upto 2 decimal places.

The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)

Find the increase per cent of sugar consumed if cream of tomato soup is chosen over sweet corn soup.

The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)

Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.

Music CD originally priced at Rs 120 is on sale for 25% off. What is the S.P.?

Sonia and Rahul have different ways of calculating the sale price for the items they bought.

As you work on the next problem, try both of these methods to see which you prefer.

Store A and Store B both charge Rs 750 for a video game. This week the video game is on sale for Rs 600 at Store B and for 25% off at Store A. At which store is the game less expensive?

At a toy shop price of all the toys is reduced to 66% of the original price.

1. What is the sale price of a toy that originally costs Rs 90?
2. How much money would you save on a toy costing Rs 90?

A store is having a 25% discount sale. Sheela has a Rs 50 gift voucher and wants to use it to buy a board game marked for Rs 320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable.

- Method 1: Subtract Rs 50 from the price and take 25% off the resulting price.

- Method 2: Take 25% off the original price and then subtract Rs 50.

1. Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.
2. For each method, calculate the amount Sheela would have to pay. Show your work.
3. Which method do you think stores actually use? Why?

Sanjay is looking for one-bedroom apartment on rent. At Neelgiri apartments, rent for the first two months is 20% off. The one-bedroom rate at Neelgiri is Rs 6,000 per month. At Savana apartments, the first month is 50% off. The one-bedroom rate at Savana apartments is Rs 7000 per month. Which apartment will be cheaper for the first two months? By how much?

For an amount, explain why, a 20% increase followed by a 20% decrease is less than the original amount.

Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes you can stay in the sun before you receive one minute of burning UV rays. For example, if you apply sunscreen with SPF 15, you get 1 minute of UV rays for every 15 minutes you stay in the sun.

A sunscreen with SPF 15 allows only `1/15` of the sun’s UV rays. What per cent of UV rays does the sunscreen abort?

Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes you can stay in the sun before you receive one minute of burning UV rays. For example, if you apply sunscreen with SPF 15, you get 1 minute of UV rays for every 15 minutes you stay in the sun.

Suppose a sunscreen allows 25% of the sun’s UV rays.

1. What fraction of UV rays does this sunscreen block? Give your answer in lowest terms.
2. Use your answer from Part (a) to calculate this sunscreen’s SPF. Explain how you found your answer.

Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes you can stay in the sun before you receive one minute of burning UV rays. For example, if you apply sunscreen with SPF 15, you get 1 minute of UV rays for every 15 minutes you stay in the sun.

A label on a sunscreen with SPF 30 claims that the sunscreen blocks about 97% of harmful UV rays. Assuming the SPF factor is accurate, is this claim true? Explain.

A real estate agent receives Rs 50,000 as commission, which is 4% of the selling price. At what price does the agent sell the property?

With the decrease in prices of tea by 15% Tonu, the chaiwallah, was able to buy 2 kg more of tea with the same Rs 45 that he spent each month on buying tea leaves for his chai shop. What was the reduced price of tea? What was the original price of tea?

Below is the Report Card of Vidit Atrey. Vidit’s teacher left the last column blank. Vidit is not able to make out, in which subject he performed better and in which he needs improvement. Complete the table to help Vidit know his comparative performance.

Sita is practicing basket ball. She has managed to score 32 baskets in 35 attempts. What is her success rate in per centage?

During school hours, Neha finished 73% of her homework and Minakshi completed 5/8 of her homework. Who must finish a greater per cent of homework?

Rain forests are home to 90,000 of the 2,50,000 identified plant species in the world. What per cent of the world’s identified plant species are found in rain forests?

Madhu’s room measures 6 m × 3 m. Her carpet covers 8 m². What per cent of floor is covered by the carpet?

The human body is made up mostly of water. In fact, about 67% of a person’s total body weight is water. If Jyoti weights 56 kg, how much of her weight is water?

The per cent of pure gold in 14 carat gold is about 58.3%. A 14 carat gold ring weighs 7.6 grams. How many grams of pure gold are in the ring?

A student used the proportion `n/100 = 5/32` to find 5% of 32. What did the student do wrong?

The table shows the cost of sunscreen of two brands with and without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate of each brand.