# Time and Work Quiz Set 017

### Question 1

A, B and C complete a work in 6, 4 and 5 days respectively. All three of them start the work together, but A leaves the work after 2 days, and B leaves the work after 1 days. In how many days will the work be completed?

A

\$2{1/12}\$ days.

B

\$3{1/12}\$ days.

C

\$4{1/12}\$ days.

D

\$5{1/12}\$ 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, and B after m days, the work is completed in z × \$(1 - n/x - m/y)\$ days. Putting the various values x = 6, y = 4, z = 5, n = 2, m = 1, and simplifying, we get \${25/12}\$, which is same as: \$2{1/12}\$.

### Question 2

If 14 men can do a task in 18 days, how many men are required to complete the task in 7 days?

A

36.

B

8.

C

6.

D

10.

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 = 14, d1 = 18 and d2 = 7, we get m2 = 36.

### Question 3

A can harvest a field in 2 days. B can do the same work in 9 days. In how many days will they together harvest the field?

A

\$1{7/11}\$ days.

B

\$2{7/11}\$ days.

C

\$3{7/11}\$ days.

D

\$4{7/11}\$ days.

Soln.
Ans: a

Putting x = 2 and y = 9 in the shortcut method, we get \${xy}/{x + y}\$ = \${18/11}\$, which is same as: \$1{7/11}\$.

### Question 4

A can harvest a field in 19 days. B can do the same work in 13 days. C can do the same work in 5 days. How much did A get if the farmer pays them a total amount of Rs. 13300 for a work that they together completed in 4 days?

A

Rs. 2800.

B

Rs. 2900.

C

Rs. 2700.

D

Rs. 3100.

Soln.
Ans: a

Work done by A in 1 day = \$1/19\$. So the work in 4 days = 4 × \$1/19\$. His share is Rs. 4 × \$1/19\$ × 13300 = Rs. 2800.

### Question 5

A new tub can be filled by a tap in 5 minutes. But the tub is worn out, and there is a leakage that can empty the tub in 13 minutes. In how many minutes will the tap be able to fill the tub?

A

\$8{1/8}\$ mins.

B

\$9{1/8}\$ mins.

C

\$10{1/8}\$ mins.

D

\$11{1/8}\$ mins.

Soln.
Ans: a

Putting x = 5 and y = 13 in the shortcut method, we get \${xy}/{y - x}\$ = \${65/8}\$, which is same as: \$8{1/8}\$.