# Time and Work Quiz Set 013

### Question 1

A and B can complete a job in 22 and 88 days. They start together but A leaves after working for 8 days. How long would B take to finish the job counting from the day both A and B started together?

A

56 days.

B

57 days.

C

55 days.

D

59 days.

Soln.
Ans: a

If B takes x days. The total job is A's work in 4 days + B's work in x days = \$8/22\$ + \$x/88\$ = 1. Solving, we get x = 56 days.

### Question 2

A can finish a work in 10 days. B can do the same work in 5 days. They work together for 3 days. The fraction of work that is left is?

A

\${1/10}\$.

B

\$1{1/10}\$.

C

\${1/9}\$.

D

\${2/11}\$.

Soln.
Ans: a

They together finish \$1/10 + 1/5\$ work in a day. In 3 days they finish 3 × \$(1/10 + 1/5)\$ work, which is \$45/50\$. So the un-finished work is 1 - \$45/50\$ = \${1/10}\$.

### Question 3

A can harvest a field in 5 days. B can do the same work in 6 days. C can do the same work in 18 days. How much did A get if the farmer pays them a total amount of Rs. 2500 for a work that they together completed in 4 days?

A

Rs. 2000.

B

Rs. 2100.

C

Rs. 1900.

D

Rs. 2300.

Soln.
Ans: a

Work done by A in 1 day = \$1/5\$. So the work in 4 days = 4 × \$1/5\$. His share is Rs. 4 × \$1/5\$ × 2500 = Rs. 2000.

### Question 4

A new tub can be filled by a tap in 9 minutes. But the tub is worn out, and there is a leakage that can empty the tub in 18 minutes. In how many minutes will the tap be able to fill the tub?

A

18 mins.

B

19 mins.

C

20 mins.

D

21 mins.

Soln.
Ans: a

Putting x = 9 and y = 18 in the shortcut method, we get \${xy}/{y - x}\$ = 18.

### Question 5

A can harvest a field in 5 days. B can do the same work in 14 days. C can do the same work in 3 days. In how many days will they together harvest the field?

A

\$1{83/127}\$ days.

B

\$2{83/127}\$ days.

C

\$3{83/127}\$ days.

D

\$4{83/127}\$ days.

Soln.
Ans: a

Putting x = 5, y = 14 and z = 3 in the shortcut method, we get \${xyz}/{xy + zy + zx}\$ = \${210/127}\$, which is same as: \$1{83/127}\$. 