# Time and Work Quiz Set 009

### Question 1

A can harvest a field in 7 days. B can do the same work in 10 days. In how many days will they together harvest the field?

A

\$4{2/17}\$ days.

B

\$5{2/17}\$ days.

C

\$6{2/17}\$ days.

D

\$7{2/17}\$ days.

Soln.
Ans: a

Putting x = 7 and y = 10 in the shortcut method, we get \${xy}/{x + y}\$ = \${70/17}\$, which is same as: \$4{2/17}\$.

### Question 2

A can finish a work in 12 days. B can do the same work in 13 days. They work together for 4 days. The fraction of work that is left is?

A

\${14/39}\$.

B

\$1{14/39}\$.

C

\${7/19}\$.

D

\${3/8}\$.

Soln.
Ans: a

They together finish \$1/12 + 1/13\$ work in a day. In 4 days they finish 4 × \$(1/12 + 1/13)\$ work, which is \$100/156\$. So the un-finished work is 1 - \$100/156\$ = \${14/39}\$.

### Question 3

A can do a work in 3 days. B can destroy the work in 7 days. In how many days will they together complete the work?

A

\$5{1/4}\$ days.

B

\$6{1/4}\$ days.

C

\$7{1/4}\$ days.

D

\$8{1/4}\$ days.

Soln.
Ans: a

Putting x = 3 and y = 7 in the shortcut method, we get \${xy}/{y - x}\$ = \${21/4}\$, which is same as: \$5{1/4}\$.

### Question 4

Mr. X can finish a task in 13 days. Mr. Y can do the same work in 8 days. What is the ratio of the efficiencies of X : Y?

A

\${8/13}\$.

B

\$1{8/13}\$.

C

\${2/3}\$.

D

\${9/14}\$.

Soln.
Ans: a

The efficiency of X is \$100/13\$%, and the efficiency of Y is \$100/8\$%, so the ratio will be \$8/13\$

### Question 5

A, B and C can independently complete a work in 5, 15 and 16 days respectively. First C starts the work, then A joined after 7 days, and B after 6 days. In how many days was the work completed?

A

\$8{40/79}\$ days.

B

\$9{40/79}\$ days.

C

\$10{40/79}\$ days.

D

\$11{40/79}\$ 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 = 5, y = 15, z = 16, n = 7, m = 6, and simplifying, we get \${672/79}\$, which is same as: \$8{40/79}\$. This Blog Post/Article "Time and Work Quiz Set 009" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-03