15-10-2021 Answers

1. A woman has a certain number of mangoes of which 13% are bad. She gives 75% of the remainder as free to children charity and then finally she has 261 left. How many mangoes did she have initially?

Answer: 1200

Solution: Let the initial number of mangoes be x.

Good mangoes = 0.87x.

As she gave 0.75*0.87x to children,

0.25*0.87x = 261,

x = 261/(0.25*0.87) = 1200

2. The price of an article was first increased by 10% and later decreased by 5%. What is the percent change in the price?

Answer: 4.5% increase

Solution: Let the initial price of the article be x.

Final revised price = x * 1.1 * 0.95 = 1.045x

Hence % increase = 100 * 0.045x/x = 4.5%

3. The price of an article is first increased by 15% and later again by 10%. Find the net percent increase in the price.

Answer: 26.5%

Solution: Let original price be x.

Revised price = x * 1.15 * 1.1 = 1.265x

Hence net % increase = 100 * 0.265x/x = 26.5%

4. The price of rice falls by 10%. By how much percent must its consumption be increased so as not to decrease expenditure.

Answer: 11(1/9)%

Solution: Let original price be x and consumption be y.

Original expense = xy

Let the increase in the consumption be k.

Revised expense = 0.9x * ky = xy

k = 1/0.9 = 10/9

Hence % increase = 100 * (10/9 - 1) = 100/9 = 11(1/9)%

5. A student get 80 marks and fails by 40 marks. If the percentage pass marks is 40% what is the maximum marks?

Answer: 300

Solution: Passmark = 80+40 = 120

As pass % is 40%,

120 = 40% of Maximum Marks.

Hence Maximum Marks = 120/0.4 = 300

6. In an election, there were only two candidates. A got 54,440 votes while B got only 48,970 votes. What percent of votes did A get?

Answer: 52.6%

Solution: Assuming all were valid votes, total votes = 54440+48970 = 103410.

% votes A got = 100 * 54440/103410 = 52.64% = 52.6% approx

7. A has Rs. 9821, which is 15% more than B but about 15% less than C. Find the amount each has

Answer: B = Rs. 8540, C = Rs. 11554 approx

Solution: 1.15*B = 9821,

B = 9821/1.15 = 8540

C*0.85 = 9821,

C = 9821/0.85 = 11554.11 = 11554 approx

8. The shopkeeper increases the price of shirts by 10%. It's sales also increased by 25%. Find the net effect on his income.

Answer: 37.5% increase

Solution: Let original price of a shirt be x and sales be y.

Original income = xy

Revised income = 1.1x * 1.25y = 1.375xy

% change = 100* 0.375xy/xy = 37.5% increase

9. If x is 90% of y, then what % of x is y?

Answer: 111.1%

Solution: x = 0.9y,

y = x/0.9 = x * 10/9.

As % it is 100 * 10/9 = 1000/9 = 111.11111% which is 111.1% approx

10. The price or sugar increases by 30%. By how much percent its consumption must be reduced so as not to increase expenditure?

Answer: 23(1/13)%

Solution: Let original price be x and consumption be y.

Original expense = xy

Let the decrease in the consumption be k.

Revised expense = 1.3x * ky = xy

k = 1/1.3 = 10/13

Hence % decrease = 100 * (1 - 10/13) = 100 * 3/13 = 300/13 = 23(1/13)%

11. Railways reduced the fare by 8% but the number of passengers decreased by 10%. What is the percent change in its revenue?

Answer: 17.2% decrease

Solution: Let original fare be x and num of passengers be y.

Original revenue = xy

Revised revenue = 0.92x * 0.9y = 0.828xy

Reduction in revenue = xy - 0.828xy = 0.172xy

Hence % change = 17.2 decrease.

12. 31% of a number is 46.5. Find the number.

Answer: 150

Solution: Let the number be x.

0.31x = 46.5,

x = 4650/31 = 150

13. The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. Find the % of slump (decrease) in the business.

Answer: 20%

Solution: Let initial business be x and revised business be y.

x * .04 = y * .05,

y = 0.8x

Decrease % = 100 * 0.2x/x = 20%

14. The tax on tobacco was increased by 10% in the budget. If consumption decreased by 5%, find the net effect on revenue.

Answer: 4.5% increase

Solution: Let original price be x and consumption be y.

Original revenue = xy

Revised income = 1.1x * 0.95y = 1.045xy

% change = 100* 0.045xy/xy = 4.5% increase.

15. Out of an inheritance of Rs. 17500, Ram invests 45% in business, 25% in land and rest he spends. Find how much he spends.

Answer: Rs. 5250

Solution: % invested in business and land = 45+25 = 70%.

Hence amount spent = 30% of 17500

= 17500 *  30/100 = 5250

16. A man donated 5% of his income to a charitable organisation and deposited 20% of the remainder in a bank. If he now has Rs. 1919 left, what is his income?

Answer: Rs. 2525

Solution: Let the man's income be x.

Money left after donation = 0.95x.

He deposited 0.2*0.95x in the bank.

Amount remaining = 0.8*0.95x = 1919,

x = 1919/(0.8*0.95) = 2525

17. The price of a TV decreased from 14000 to 13300. Find the % decrease

Answer: 5%

Solution: Decrease = 14000 - 13300 = 700.

% decrease = 100 * 700/14000 = 5%

18. The population of a town is 160000. If the males increase by 6% and the females by 10%, the total population will increase to 172000. Find the number of females.

Answer: 60,000

Solution: Let the number of males be M and females be F.

M + F = 160000, M = 160000-F - Eqn 1

.06M + .1F = 172000-160000 = 12000

.06*(160000 - F) + .1F = 12000,

0.04F = 12000 - 9600 = 2400,

F = 2400/.04 = 60000

19. Raj deposits 12.5% of his salary in provident fund and spends 70% of the remainder. Finally, he is left with Rs. 210. What is his salary?

Answer: Rs.800

Solution: Let Raj's salary be x.

Money left after investing in provident fund = 0.875x.

He spends 0.7*0.875x.

Amount remaining = 0.3*0.875x = 210,

x = 700/0.875 = 800

20. A shopkeeper decreases the price of a shirt by 10% and later gives a discount of 20% too. What is net percent decrease in the price?

Answer: 28%

Solution: Let the initial price of the shirt be x.

Final revised price = x * 0.9 * 0.8 = 0.72x

Hence % decrease = 100 * 0.28x/x = 28%