**Find solutions for all the questions at the end of each set:**

### Set A

1. A can do a piece of work in 24 days, B in 52 days and C in 64 days. All being to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last (approx.)?

(a) 25

(b) 20

(c) 18

(d) 30

2. The least positive integer that should be subtracted from 3011×3012 so that the difference is a perfect square is-

(a) 3009

(b) 2010

(c) 3011

(d) 3012

3. While selling, a business man allows 40% discount on the marked price and there is a loss of 30%. If it is sold at the marked price, profit percent will be –

(a) 10%

(b) 20%

(c) 16 2/3%

(d) 16 1/3%

4. A cistern has 3 pipes A, B and C. A and B can fill it in 3 hours and 4 hours respectively and C can empty it in 1 hour. If the pipes are opened at 3 pm, 4 pm and 5 pm respectively on the same day, the cistern will be empty at?

(a) 7 : 12 pm

(b) 7 : 15 pm

(c) 7 : 10 pm

(d) 7 : 18 pm

5. 250 men can finish a work in 20 days working 5 hours a day. To finish the work within 10 days working 8 hours a day, the minimum number of men required is –

(a) 310

(b) 300

(c) 313

(d) 312

6. 2 men and 5 women can do a work in 12 days. 5 men and 2 women can do that work in 9 days. Only 3 women can finish the same work in –

(a) 36 days

(b) 21 days

(c) 30 days

(d) 42 days

7. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is –

(a) 5 : 3

(b) 3 : 5

(c) 3 : 4

(d) 4 : 3

8. A and B earn in the ratio 2 : 1. They spend in the ratio 5 : 3 and save in the ratio 4 : 1. If the total monthly savings of both A and B are Rs. 5000, the monthly income of B is –

(a) Rs. 7000

(b) Rs. 14000

(c) Rs. 5000

(d) Rs. 10000

9. The ratio of the sum of two numbers and their difference is 5 : 1. The ratio of the greater number to the smaller number is –

(a) 2 : 3

(b) 3 : 2

(c) 5 : 1

(d) 1 : 5

10. An employer reduces the number of his employees in the ratio 9 : 8 and increase their wages in the ratio 14 : 15. If the original wage was Rs. 18900, find the ratio in which the wage bill is decreased.

(a) 20 : 21

(b) 21 : 20

(c) 20 : 19

(d) 19 : 21

ANSWERS and SOLUTIONS:

1- (a)

Let the work is completed in n days.

then,

6/24+(n-6)/52+n/64 = 1

n = 720/29 = 25 days

2- (c)

Required number

= 3012*3011-(3011)^2

= 3011(3012-3011)

= 3011

3- (c)

Let CP = x

then,

SP = 70% of x = 0.7x

=> 60% of MP = 0.7x

= MP = 0.7x/60*100 = 7x/6

If article is sold at the marked price,

then

SP = 7/6 x

so Required profit percent

(7/6x-x)/x * 100%

= 100/6% = 16 2/3%

4- (a)

5- (c)

Here,M1 = 250,D1=20,T1=5

M2 = ? ,D2= 10, T2 = 8

using M1D1T1 = M2D2T2 , we have

250*20*5 = M2*10*8

M2 = 313

6- (a)

7- (a)

8- (a)

9- (b)

10- (b)

Ratio of reduction is number of employees = 9:8

Ratio of increment in wages = 14:15

Now, ratio of reduction in the wage bill

= 9*14 : 8*15

= 126 : 120

= 21 : 20

**Find solutions for all the questions at the end of each set:**

### Set B

1. A stock of food grain is enough for 500 persons for 8 weeks. How long will the same stock last for 400 persons?

(a) 9 weeks

(b) 10 weeks

(c) 15 weeks

(d) 20 weeks

2. If the marked price of an item is 1.5 times its cost price and it is sold at 10% loss, then the percentage of discount is

(a) 10%

(b) 20%

(c) 30%

(d) 40%

3. The prices of two articles are as 3 : 4. If the price of the first article be increased by 10% and that of the second by Rs. 4, the original ratio remains the same. The original price (in Rs.) of the second article is

(a) 10

(b) 30

(c) 50

(d) 40

4. The monthly incomes of P and Q are as 5 : 6 and the monthly expenditures are as 4 : 5. If both of them save Rs. 500 every month, the monthly income of P (in Rs.) is

(a) 2,400

(b) 2,800

(c) 3,000

(d) 2,500

5. Two bags contain marbles in the ratio of 3 : 4. If 4 marbles are transferred from the second bag to the first, the number of marbles in the two bags becomes equal. The number of marbles in each bag is

(a) 12 and 16

(b) 24 and 32

(c) 15 and 20

(d) 18 and 24

6. In a mixture of 25 litres, the ratio of two liquids A and B is 4 : 1. If 2 litres of liquid A and 3 litres of liquid B are added to it what is the new ratio of A and B?

(a) 11 : 4

(b) 4 : 11

(c) 9 : 4

(d) 4 : 9

7. Two vessels A and B contain milk and water in the ratio of 5 : 3 and 2 : 3. When these mixture are mixed to form a new mixture containing half milk and half water, they must be take in the ratio of

(a) 2 : 5

(b) 3 : 5

(c) 4 : 5

(d) 7 : 3

8. The mean temperature of Monday to Wednesday was 37°C.and of Tuesday to Thursday was 34°C. If the temperature on Thursday was 4/5th that of Monday, the temperature on Thursday was

(a) 36°C

(b) 35.5°C

(c) 36.5°C

(d) 35°C

9. A man had 5 children, When their average age was 10 years, the child who was of 5 years of age died. What was the average age (in years) of the surviving children 4 years after the death of the child?

(a) 15 1/4

(b) 14 3/4

(c) 15

(d) 14

10. In nine numbers the average of the first five numbers is 5 and that of the last five numbers is also 5. If the average of these nine number is 4, the fifth number is

(a) 9

(b) 11

(c) 4

(d) 14

ANSWERS AND SOLUTIONS:

1- (b)

M1D1 = M2D2

500*8 = 400*D2

D2 = 10 days

2- (d)

Let cost price = Rs.100

Marked price = Rs.(100*1.5) = 150

Selling price = (100*90/100) = 90

Discount offered = (150-90)/150 * 100 = 40%

3- (d)

4- (d)

5- (b)

6- (a)

Liquid of A in original mixture = 4/5*25 = 20 litres

Liquid of B in original mixture = 1/5*25 = 5 litres

Required ratio = (20+2) : (5+3) = 11:4

7- (c)

8- (a)

9- (a)

ATQ,

Average Age = ((5*10-5)+4*4)/4 = 15 (1/4) years

10- (d)

ATQ,

Fifth number=(5*5)+(5+5)-9*4 = 14