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

### Set A

1.The ratio of number of boys to that of girls in a group becomes 2 : 1 when 15 girls leave. But, afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was

(1) 20

(2) 30

(3) 40

(4) 50

2.The area of the largest triangle, that can be inscribed in a semicircle of radius r cm is

(1) 2r cm^2

(2) r^2 cm^2

(3) 2r^2 cm^2

(4) 1/2r^2 cm^2

3. 12 persons can do a piece of work in 4 days. How many persons are required to complete 8 times the work in half the time?

(1) 192

(2) 190

(3) 180

(4) 144

4. Two pipes can fill a tank in 15 hours and 20 hours respectively, while the third can empty it in 30 hours. If all the pipes are opened simultaneously, the empty tank will be filled in

(1) 10 hours

(2) 12 hours

(3) 15 hours

(4) 15 1/2 hours

5.The difference between the interior and exterior angles of a regular polygon is 60. The number of sides in the polygon is :

(1) 4

(2) 5

(3) 6

(4) 8

6. A Person bought some articles at the rate of 5 per rupee and the same number at the rate of 4 per rupee. He mixed both the types and sold at the rate of 9 for 2 rupees. In this business he suffered a loss of Rs. 3. The total number of articles bought by him was

(1) 1090

(2) 1080

(3) 540

(4) 545

7. A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave?

(1) 10 days

(2) 9 days

(3) 8 days

(4) 5 days

8. An individual pays 30% income tax. On this tax he has to pay a surcharge of 10%. Thus, the net tax rate, he has to pay, is

(1) 45%

(2) 40%

(3) 33%

(4) 27%

9. If the price of tea is increased by 20%, by how much per cent the consumption of tea be reduced so that there is no increase in the expenditure on it?

(1) 831/3%

(2) 20%

(3) 162/3%

(4) 81/3%

10.The principal, which will amount to Rs. 270.40 in 2 years at the rate of 4% per annum compound interest, is

(1) Rs. 200

(2) Rs. 225

(3) Rs. 250

(4) Rs. 220

Answers and Solution:

1. (3)

let the original number of boys and girls be x and y respectively

then

x/y-15 = 2/1

=> x = 2y-30

Again, (x-45)/(y-15) = 1/5

=> 5x – 225 = y-15

after solve we get

so y = 40

2.(2)

3. (1)

12 persons can complete a work in 4 days.

=> 24 persons can complete the work in 2 days.

=> 24 persons can complete the 8 times work in 16 days.

=> 24*8 persons = 192 persons can complete.

4.(2)

part of tank filled in 1 hour when all three pipe are opened simultaneously

= 1/15 + 1/20 – 1/30 = 1/12

Hence, the tank will be filled in 12 hours

5.(3)

6. (2)

let the person buy 10 articles.

Total CP = Rs.(1+5/4) = Rs.9/4

SP of 10 articles

= Rs. 2/9 *10 = Rs.20/9

so Loss = (9/4 – 20/9)= 1/36

Now, if loss is Rs.1/36 ,number of article = 10

so If loss is Rs.3 ,number of article = 36*10*3 = 1080

7. (2)

8. (3)

The net tax rate = (30+30*10/100)% = 33%

9. (3)

10. (3)

let the principal be Rs. p

so 270.40= p(1+4/100)^2

p = Rs.250

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

### Set B

1. Mohan and Sohan can do a job in 12 days. Sohan alone can finish it in 28 days. In how many days can Mohan alone finish the work?

(1) 25 days

(2) 21 days

(3) 18 days

(4) 15 days

2.Mary and Maurice can do a piece of work in 10 days and 15 days respectively. They work together for 3 days and then Maurice leaves. Mary finishes the remaining work alone. In how many days is the total work finished?

(1) 5 days

(2) 2 days

(3) 8 days

(4) 10 days

3.A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would each take separately to do the same work?

(1) A-30 days,B-20 days,C-60 days

(2) A-20 days,B-30 days,C-60 days

(3) A-60 days,B-20 days,C-30 days

(4) A-20 days,B-60 days,C-30 days

4.Keberi takes twice as much time as Kanti and thrice as much as kalpana to finish a piece of work. They together finish the work in one day. Find the time taken by each of them to finish the work.

(1) Kaberi = 6 days,Kanti = 4 days, kalpana = 2 days

(2) Kaberi = 4 days,Kanti = 3 days, kalpana = 6 days

(3) Kaberi = 4 days,Kanti = 6 days, kalpana = 3 days

(4) Kaberi = 6 days,Kanti = 3 days, kalpana = 2 days

5.A, B and C can do a work in 10, 12 and 15 days, respectively. If B leaves after 2 days, how long would it take A and C to complete the remaining work?

(1) 3 days

(2) 6 days

(3) 1 days

(4) 5 days

6.P can do a work in 12 days. Q works 60% more fast then P, then in how many days Q alone would finish the work?

(1) 7 (3/2)days

(2) 8 (1/2)days

(3) 6 days

(4) 7 (1/2) days

7. Suresh can do 3/4 th part of a work in 15 days and Mohan completes the rest part of work in 3 days, in how many days Suresh and Mohan together can finish the work

(1) 25/5 days

(2) 21/2 days

(3) 18 days

(4) 15/2 days

8.Ramesh is thrice as good as workman as Bipan, and is therefore able to finish a piece of work in 40 days less than Bipan, find the time for both together to complete the work

(1) 12 days

(2) 15 days

(3) 18 days

(4) 13 days

9.If 3 men or 4 women can complete a job in 43 days then in how many days 7 men and 5 women can complete the some job?

(1) 12 days

(2) 11 days

(3) 14 days

(4) 10 days

10.If 5 men and 2 Women working together can make bricks four times more than a man and a woman working together. Compare the work of a man with that of a woman.

(1) 2/1

(2) 1/2

(3) 2/3

(4) 3/2

Answers and Solution:

1.(2)

Mohan and sohan do work in = 12 days

sohan do work in = 28 days

so Mohan do work alone = 1/12 – 1/28 = 1/21 of work

mohan’s alone time = 1/1/21 = 21 days

2.(3)

Mary’s efficiency = 10%

Maurice’s efficiency = 6.66%

Total = 16.66%

Work will be completed in 6 days

Work done in 3 days = 50%

remaining = 50%

Mary will complete the remaining in = 50/10 = 5

Total = 5+3 = 8 days

3.(1)

4.(4)

Let alone time of Kaberi = x,

then alone time of kanti = x/2 and

kalpana = x/3

Kaberi’s 1 day work + kanti’s 1 day work+ kalpana’s 1 day work

=> 1/x + 1/x/2 + 1/x/3 = 1

=> x = 6

so alone time of Kaberi = 6 days

alone time of Kanti = 3 days

alone time of Kalpana = 2 days

5. (1)

6. (4)

p’s 1 day work = 1/12

Q is 60% more fast then p, so Q’s 1 day work = 1.6*1/12 = 2/15

Q can finish alone in 1/2/15 = 15/2 = 7(1/2) days

7. (4)

8. (2)

Since Ramesh is thrice as good a workman as Bipin .So ,if Bipin completes in 3t days,then Ramesh does in t days

so 3t – t = 40

=> t = 20

=> Bipin takes 60 days and Ramesh takes 20 days (Ramesh+Bipin)’s 1 day work

=> 1/60 + 1/20 = 1/15 = 15 days.

9.(1)

10.(1)

(5M +2W)’s 1 day work = (1M +1W)’s 4 day work

5M + 2W = 4(1M+1W)

5M + 2W = 4M + 4W

1M + 2W

M/W = 2/1