# Time and Work Quiz Set 015

### Question 1

A and B can together complete a job in 10 days. A can alone complete it in 15 days. How long would B alone take to finish the job?

A

30 days.

B

31 days.

C

29 days.

D

33 days.

Soln.
Ans: a

One day work of A + B is \$1/10\$. One day work of A is \$1/15\$. So one day work of B, say, \$1/y\$ = \$1/10\$ - \$1/15\$. Solving, we get y = 30 days.

### Question 2

If 45 men can do a task in 5 days, how many men are required to complete the task in 9 days?

A

25.

B

10.

C

8.

D

12.

Soln.
Ans: a

If m1 men can do a task in d1 days, and m2 in d2, then we must have m1 × d1 = m2 × d2. Putting m1 = 45, d1 = 5 and d2 = 9, we get m2 = 25.

### Question 3

A and B can together complete a job in 16 days. A can alone complete it in 24 days. How long would B alone take to finish the job?

A

48 days.

B

49 days.

C

47 days.

D

51 days.

Soln.
Ans: a

One day work of A + B is \$1/16\$. One day work of A is \$1/24\$. So one day work of B, say, \$1/y\$ = \$1/16\$ - \$1/24\$. Solving, we get y = 48 days.

### Question 4

A, B and C complete a work in 9, 3 and 19 days respectively. All three of them start the work together, but A leaves the work after 1 days. In how many days will the work be completed?

A

\$2{10/33}\$ days.

B

\$3{10/33}\$ days.

C

\$4{10/33}\$ days.

D

\$5{10/33}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A leaves after n days, the work is completed in \${yz}/{y + z}\$ × \$(1 - n/x)\$ days. Putting the various values x = 9, y = 3, z = 19, n = 1, and simplifying, we get \${76/33}\$, which is same as: \$2{10/33}\$.

### Question 5

A, B and C can independently complete a work in 16, 3 and 13 days respectively. First C starts the work, then A joined after 1 days, and B after 2 days. In how many days was the work completed?

A

\$3{194/295}\$ days.

B

\$4{194/295}\$ days.

C

\$5{194/295}\$ days.

D

\$6{194/295}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A joins after n days, and B joins after m days, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x + m/y)\$ days. Putting the various values x = 16, y = 3, z = 13, n = 1, m = 2, and simplifying, we get \${1079/295}\$, which is same as: \$3{194/295}\$. 