A.34.5 days

B.37.2 days

C.39.5 days

D.41.3 days

E.43.9 days

2) 20 women can complete the work in 26 days. If 32 boys started the work and after x days 8 more boys joined the work and completed the remaining work in 7 days. Find the value of x.

A.7.5

B.12.5

C.9

D.15

E.8

3) A alone completes the work in (x + 8) days and B alone completes the work in (x - 2) days. If A and B together can complete the work in (x – 10) days, find the value of x?

A.10

B.15

C.12

D.18

E.22

4) Ravi is 20% more efficient than Ram who is 10% more efficient than Raghu. If Raghu, Ram and Ravi together can complete a piece of job in 50 days, then in how many days Ram alone can complete 33% of the job?

A.51.3 days

B.65.2 days

C.71 days

D.91 days

E.None of these

5) A and B together can complete the work in x days and A alone complete the work in (x + 5) days. B takes 15 days more than A to do the same work. Find the value of x?

A.10

B.15

C.8

D.12

E.20

Answers :

1) Answer: B

A + B + C = 1/30

A = 5/6 B

A/B = 5/6

C = 75/100 * B

C/B = 3/4

Efficiency of A, B and C = 10:12:9

Total work = 30 * 31

Required time = (84/100 * 31 * 30)/21

= 37.2 days

2) Answer: A

Total work = 20 * 26 = 520

Total work done by 40 boys in 7 days = 40 * 7 = 280

x = (520 – 280)/32 = 7.5 days

3) Answer: E

1/(x + 8) + 1/(x – 2) = 1/(x – 10)

((x – 2) + (x + 8)) * (x – 10) = (x – 2) * (x + 8)

2x² + 6x – 20x – 60 = x² + 8x – 2x – 16

x² – 20x – 44 = 0

x² – 22x + 2x – 44 = 0

x(x – 22) + 2(x – 22) = 0

x = 22(Neglecting negative number of days)

4) Answer: A

Number of units work done by Raghu = a units

Number of units work done by Ram = 1.10a

Number of units work done by Ravi = 1.10a * 1.20 = 1.32a

Total work = 50 * (a + 1.10a + 1.32a) = 171a

Time taken by Ram to complete 33% = (0.33 * 171a)/1.10a

=> 51.3 days

5) Answer: A

1/A + 1/B = 1/x

1/A = 1/(x + 5)

1/B = 1/(x + 5 + 15)

1/(x + 5) + 1/(x + 20) = 1/x

((x + 20) + (x + 5))/(x + 5) * (x + 20) = 1/x

2x² + 25x = x² + 20x + 5x + 100

x² = 100

x = 10, -10