**Question: 6 Adults can do a job twice as faster as children. If X adults can complete a job in a day, how many children can do the same job in (d + 2) days?**

Option: (a) 2dx/(d +2) (b) (d + 2)x/d (c) dx/2(d + x) (d) (2x + d)/(d - x) (e) None of these

Explore:

X adults can do the job in d days

:. 2X children can do the job in d days

:. 2xd children can do the job in d days

:. (2xd)/(d + 2) children can do the job in (d + 2) days

Answer : (a)

**Question: 7 Mr. X can finish a work in 6 days and Mr. Ly can finish the same work in 8 days. How long will it take to finish the work together?**

Explore:

Mr. X in 6 days can finish 1 portion

:. Mr. X in 1 days can finish 1/6 portion

Mr. y in 8 days can finish 1 portion

:. Mr. y in 1 days can finish 1/8 portion

:. In 1 day X & Y can finish (1/6 + 1/8) Portion

= (4 + 3)/24

= 7/24

:. X & Y together finish 7/24 portion in 1 day

:. X & Y together finish 1 portion in (1 x 24)/7

= 24/7

= 3(3/7) days

Answer : 3(3/7) days

**Question: 8 A can dig a pond in 30 days and B can dig the same pond in 20 days. In how many days A and B can dig the pond if they work together?**

Explore:

A in 30 days can dig 1 portion

:. A in 1 days can dig 1/30 portion

B in 20 days can dig 1 portion

:. B in 1 days can dig 1/20 portion

A & B together in 1 day can dig (1/30 + 1/20) portions

= (2 + 3)/60 portion

= 5/60 portion

= 1/12 Portion

A & B together can dig 1/12 portion in 1 day

:. A & B together can dig 1 portion in (1 x 13)/1 day

= 12 day

Answer : A & B together can dig in 12 days.

**Question: 9 Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1(1/2) hours. How quickly can all the three fill the poll together?**

Option: (a) 12 minutes (b) 15 minutes (c) 21 minutes (d) 23 minutes (e) 28 minutes

Explore:

1(1/2) hours = 60 + 30 Minutes

= 90 minutes

Jim in 30 minutes can do 1 portion

:. Jim in 1 minutes can do 1/30 portion

Similarly,

Sue in 1 minutes can do 1/45 portion

& Tony in 1 minutes can do 1/ 90 portion

Together all the three in 1 minute can do (1/30 + 1/45 + 1/90) portion

= (3+2+1)/90

= 6/90

= 1/15

Together 1/15 portion is finished in 1 minute

:. Together 1 portion is finished in (1 x 15)/1 minutes

= 15 minutes

Answer : (b)

**Question: 10 A and B can do a work in 12 days. B and C can do it in 15 days. and A and C can do it in 20 days. If all of them work together, in how many days they can finish the work?**

Option: (a) 25 (b) 9 (c) 12 (d) 10 (e) 22

Explore:

A & B in 12 days can do 1 portion

:. A & B in 1 days can do 1/12 portion

B & C in 15 days can do 1 portion

:. B & C in 1 days can do 1/15 portion

A & C in 20 days can do 1 portion

:. A & C in 1 days can do 1/20 portion

:. 2A, 2B and 2C in 1 day can do (1/12 + 1/15 + 1/20) portion

= (5 + 4 + 3)/60

= 12/60

= 1/5 portion

:. 2A, 2B & 2C can finish 1/5 portion in 1 day

:. 2A, 2B & 2C can finish 1 portion in (1 x 5)/1 day

:. A, B & C can finish 1 portion in (5 x 2) = 10 days

Answer : (d)