## RS Aggarwal Class 8 Math Ninth Chapter Percentage Exercise 9A Solution

## EXERCISE 9A

**(1) Express each of the following as a fraction:**

**(2) Express each of the following as a decimal:**

**(3) Express each of the following s a percentage:**

**(4) Convert the ratio 4 : 5 to percentage.**

**(5) Express 125% as a ratio.**

**(7)(i) What per cent of 150 is 96?**

**(ii) What per cent of 5 kg is 200 g?**

**(iii) What per cent of 2 litres is 250 ml?**

**(9) If 16% of a number is 72, find the number.**

Solution: Let the required number be x. Then,

16% of x = 72

Hence, the required number is 450.

**(10) A man saves 18% of his monthly income. If he saves Rs 3780 per month, what is his monthly income?**

Solution: Let his monthly income be Rs x.

Hence, the monthly income of the man is Rs 21000.

**(11) A football team wins 7 games, which is 35% of the total games played. How many games were played in all?**

Solution: Let the number of playing game be x.

Hence, the team 20 games were played in all.

**(12) Amit was given an increment of 20% on his new salary is Rs 30600, what was his salary before the increment?**

Solution: Let Amit’s salary before his increment be Rs x.

**(13) Sonal attended her school on 204 days in full year. If her attendance is 85%, find the number of days on which the school was opened.**

Solution: Let the numbers of days on which the school was opened be x days.

Then, (85/100)×x

⇒ 85x = 20400

⇒ x = 240

Hence, the number of days which Sonal’s school was opened is 240 days.

**(14) A’s income is 20% less than that B. By what per cent is B’s income more than A’s?**

Solution: Let B’s income be Rs 100.

Then, A’s income = Rs (100 – 20) = Rs 80.

If A’s income is Rs 80, then B’s income = Rs 100.

If A’s income is Rs 100, then B’s income = Rs [(100/80)×100]=Rs 125.

∴ B’s income more than A’s income by (125 – 100) = 25%.

**(15) The price of petrol goes up by 10%. By how much per cent must a motorist reduce the consumption of petrol so that expenditure on it remains unchanged?**

Solution: Let the consumption of petrol originally be 1 and let its cost be Rs 100.

New cost of 1 unit = Rs 110.

Now, Rs 110 yield 1 unit of petrol.

**(16) The population of a town increases by 8% annually. If the present population is 54000, what was it a year ago?**

Solution: Let the population of the town a year ago be x.

**(17) The value of a machine depreciates every year by 20%. If the present value of the machine be Rs 160000, what was its value last year?**

Solution: Let the value of the machine last year be Rs x.

**(18) An alloy contains 40% copper, 32% nickel and rest zinc. Find the mass of zinc in one kg of the alloy.**

Solution: mass of the alloy = 1 kg = 1000 g

Sum of percentage of the copper and nickel = (40 + 32) % = 72%

∴ Percentage of zinc = (100 – 72)% = 28%

∴ Mass of the zinc in 1 kg alloy = [(28/100)×1000]g=280 g.

**(19) Balanced diet should contain 12% of proteins, 25% of fats and 63% of carbohydrates. If a child needs 2600 calories in his food daily, find in calories the amount of each of these in his daily food intake.**

**(20) Gunpowder contains 75% nitre and 10% sulphur. Find the amount of gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.5 kg sulphur?**

Solution: Let the amount of the gunpowder be x.

Now, x kg be the amount of gunpowder containing 9 kg of nitre.

Hence, 12 kg of gunpowder contains 9 kg of nitre.

Now, x kg be the amount of gunpowder containing 2.5 kg of sulphur.

Hence, 25 kg of gunpowder contains 2.5 kg sulphur.

**(21) Divide Rs 7000 among A, B and C such that A gets 50% of what B gets 50% of what C gets.**

Solution: Let Rs x be the amount of money received by C.

⇒ 175x = 700000

⇒ x = 40000

∴ C get Rs 4000.

**(22) Find the percentage of pure gold in 22 carat gold, if 24-carat gold is 100% pure.**

**(23) The salary of an officer is increased by 25%, By what per cent should the new salary be decreased to restore the original salary?**

Solution: Let the salary be Rs 100.

⇒ – x = 80 – 100

⇒ – x = – 20

⇒ x = 20

Therefore, the new salary be decreased to restore the original salary by 20%.

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