# Time and Work Quiz Set 011

### Question 1

A can harvest a field in 15 days. B can do the same work in 8 days. C can do the same work in 17 days. How much did A get if the farmer pays them a total amount of Rs. 12000 for a work that they together completed in 5 days?

A

Rs. 4000.

B

Rs. 4100.

C

Rs. 3900.

D

Rs. 4300.

Soln.
Ans: a

Work done by A in 1 day = \$1/15\$. So the work in 5 days = 5 × \$1/15\$. His share is Rs. 5 × \$1/15\$ × 12000 = Rs. 4000.

### Question 2

A can do a work in 2 days. B can destroy the work in 7 days. In how many days will they together complete the work?

A

\$2{4/5}\$ days.

B

\$3{4/5}\$ days.

C

\$4{4/5}\$ days.

D

\$5{4/5}\$ days.

Soln.
Ans: a

Putting x = 2 and y = 7 in the shortcut method, we get \${xy}/{y - x}\$ = \${14/5}\$, which is same as: \$2{4/5}\$.

### Question 3

A new tub can be filled by a tap in 14 minutes. But the tub is worn out, and there is a leakage that can empty the tub in 19 minutes. In how many minutes will the tap be able to fill the tub?

A

\$53{1/5}\$ mins.

B

\$54{1/5}\$ mins.

C

\$55{1/5}\$ mins.

D

\$56{1/5}\$ mins.

Soln.
Ans: a

Putting x = 14 and y = 19 in the shortcut method, we get \${xy}/{y - x}\$ = \${266/5}\$, which is same as: \$53{1/5}\$.

### Question 4

A, B and C complete a work in 10, 13 and 19 days respectively. All three of them start the work together, but A leaves the work after 3 days, and B leaves the work after 5 days. In how many days will the work be completed?

A

\$5{129/130}\$ days.

B

\$6{129/130}\$ days.

C

\$7{129/130}\$ days.

D

\$8{129/130}\$ 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 = 10, y = 13, z = 19, n = 3, m = 5, and simplifying, we get \${779/130}\$, which is same as: \$5{129/130}\$.

### Question 5

A, B and C can independently complete a work in 17, 18 and 4 days respectively. B and C start the work together, but A joins them after 2 days. In how many days will the work be completed?

A

\$3{15/223}\$ days.

B

\$4{15/223}\$ days.

C

\$5{15/223}\$ days.

D

\$6{15/223}\$ 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, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x)\$ days. Putting the various values x = 17, y = 18, z = 4, n = 2, and simplifying, we get \${684/223}\$, which is same as: \$3{15/223}\$. 