# Time and Work Quiz Set 003

### Question 1

A can finish a work in 6 days. B can do the same work in 15 days. They work together for 4 days. The fraction of work that is left is?

A

\${1/15}\$.

B

\$1{1/15}\$.

C

\${1/14}\$.

D

\${1/8}\$.

Soln.
Ans: a

They together finish \$1/6 + 1/15\$ work in a day. In 4 days they finish 4 × \$(1/6 + 1/15)\$ work, which is \$84/90\$. So the un-finished work is 1 - \$84/90\$ = \${1/15}\$.

### Question 2

A, B and C complete a work in 9, 3 and 19 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

\$2{10/33}\$ days.

B

\$3{10/33}\$ days.

C

\$4{10/33}\$ days.

D

\$5{10/33}\$ 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 = 9, y = 3, z = 19, n = 1, and simplifying, we get \${76/33}\$, which is same as: \$2{10/33}\$.

### Question 3

Mr. X can finish a task in 7 days. Mr. Y can do the same work in 4 days. What is the ratio of the efficiencies of X : Y?

A

\${4/7}\$.

B

\$1{4/7}\$.

C

\${2/3}\$.

D

\${5/8}\$.

Soln.
Ans: a

The efficiency of X is \$100/7\$%, and the efficiency of Y is \$100/4\$%, so the ratio will be \$4/7\$

### Question 4

A can do a piece of work in 11 days. B is 10% more efficient than A. In how many days can B complete that work?

A

10 days.

B

11 days.

C

9 days.

D

12 days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/11\$. If B is 10% efficient, then one day work of B is \$1/11\$ × \$110/100\$ = \$1/10\$. Which gives 10 days as the answer.

### Question 5

A can do a piece of work in 11 days. B is 10% more efficient than A. In how many days will they complete the work if they work together?

A

\$5{5/21}\$ days.

B

\$5{2/7}\$ days.

C

\$5{1/3}\$ days.

D

\$5{8/21}\$ days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/11\$. If B is 10% efficient, then one day work of B is \$1/11\$ × \$110/100\$ = \$1/10\$. Putting x = 11 and y = 10 in the shortcut method, we get \${xy}/{x + y}\$ = \${110/21}\$, which is same as: \$5{5/21}\$.