# Time and Work Quiz Set 002

### Question 1

Mr. X can finish a task in 15 days. Mr. Y can do the same work in 17 days. What is the ratio of the efficiencies of X : Y?

A

\$1{2/15}\$.

B

\$2{2/15}\$.

C

\$1{3/14}\$.

D

\$1{1/8}\$.

Soln.
Ans: a

The efficiency of X is \$100/15\$%, and the efficiency of Y is \$100/17\$%, so the ratio will be \$17/15\$

### Question 2

A, B and C complete a work in 16, 10 and 18 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

\$6{3/112}\$ days.

B

\$7{3/112}\$ days.

C

\$8{3/112}\$ days.

D

\$9{3/112}\$ 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 = 16, y = 10, z = 18, n = 1, and simplifying, we get \${675/112}\$, which is same as: \$6{3/112}\$.

### Question 3

A new tub can be filled by a tap in 2 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

\$2{4/11}\$ mins.

B

\$3{4/11}\$ mins.

C

\$4{4/11}\$ mins.

D

\$5{4/11}\$ mins.

Soln.
Ans: a

Putting x = 2 and y = 13 in the shortcut method, we get \${xy}/{y - x}\$ = \${26/11}\$, which is same as: \$2{4/11}\$.

### Question 4

A can harvest a field in 10 days. B can do the same work in 16 days. C can do the same work in 14 days. How much did A get if the farmer pays them a total amount of Rs. 6000 for a work that they together completed in 2 days?

A

Rs. 1200.

B

Rs. 1300.

C

Rs. 1100.

D

Rs. 1500.

Soln.
Ans: a

Work done by A in 1 day = \$1/10\$. So the work in 2 days = 2 × \$1/10\$. His share is Rs. 2 × \$1/10\$ × 6000 = Rs. 1200.

### Question 5

A can harvest a field in 6 days. B can do the same work in 12 days. How much did A get if the farmer pays them a total amount of Rs. 3000 for a work that they together completed in 3 days?

A

Rs. 1500.

B

Rs. 1600.

C

Rs. 1400.

D

Rs. 1800.

Soln.
Ans: a

Work done by A in 1 day = \$1/6\$. So the work in 3 days = 3 × \$1/6\$. His share is Rs. 3 × \$1/6\$ × 3000 = Rs. 1500.