# Time and Work Quiz Set 006

### Question 1

A can harvest a field in 7 days. B can do the same work in 9 days. How much did A get if the farmer pays them a total amount of Rs. 4900 for a work that they together completed in 3 days?

A

Rs. 2100.

B

Rs. 2200.

C

Rs. 2000.

D

Rs. 2400.

Soln.
Ans: a

Work done by A in 1 day = \$1/7\$. So the work in 3 days = 3 × \$1/7\$. His share is Rs. 3 × \$1/7\$ × 4900 = Rs. 2100.

### Question 2

A, B and C complete a work in 8, 18 and 19 days respectively. All three of them start the work together, but A leaves the work after 3 days. In how many days will the work be completed?

A

\$5{115/148}\$ days.

B

\$6{115/148}\$ days.

C

\$7{115/148}\$ days.

D

\$8{115/148}\$ 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 = 8, y = 18, z = 19, n = 3, and simplifying, we get \${855/148}\$, which is same as: \$5{115/148}\$.

### Question 3

A can finish a work in 15 days. B can do the same work in 11 days. They work together for 4 days. The fraction of work that is left is?

A

\${61/165}\$.

B

\$1{61/165}\$.

C

\${61/164}\$.

D

\${31/83}\$.

Soln.
Ans: a

They together finish \$1/15 + 1/11\$ work in a day. In 4 days they finish 4 × \$(1/15 + 1/11)\$ work, which is \$104/165\$. So the un-finished work is 1 - \$104/165\$ = \${61/165}\$.

### Question 4

A, B and C can independently complete a work in 18, 11 and 13 days respectively. First C starts the work, then A joined after 4 days, and B after 1 days. In how many days was the work completed?

A

\$5{101/115}\$ days.

B

\$6{101/115}\$ days.

C

\$7{101/115}\$ days.

D

\$8{101/115}\$ 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 = 18, y = 11, z = 13, n = 4, m = 1, and simplifying, we get \${676/115}\$, which is same as: \$5{101/115}\$.

### Question 5

A, B and C can independently complete a work in 4, 18 and 16 days respectively. B and C start the work together, but A joins them after 3 days. In how many days will the work be completed?

A

\$4{40/53}\$ days.

B

\$5{40/53}\$ days.

C

\$6{40/53}\$ days.

D

\$7{40/53}\$ 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 = 4, y = 18, z = 16, n = 3, and simplifying, we get \${252/53}\$, which is same as: \$4{40/53}\$.