# Time and Work Quiz Set 010

### Question 1

A new tub can be filled by a tap in 13 minutes. But the tub is worn out, and there is a leakage that can empty the tub in 17 minutes. In how many minutes will the tap be able to fill the tub?

A

\$55{1/4}\$ mins.

B

\$56{1/4}\$ mins.

C

\$57{1/4}\$ mins.

D

\$58{1/4}\$ mins.

Soln.
Ans: a

Putting x = 13 and y = 17 in the shortcut method, we get \${xy}/{y - x}\$ = \${221/4}\$, which is same as: \$55{1/4}\$.

### Question 2

A can do a piece of work in 39 days. B is 30% more efficient than A. In how many days can B complete that work?

A

30 days.

B

31 days.

C

29 days.

D

32 days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/39\$. If B is 30% efficient, then one day work of B is \$1/39\$ × \$130/100\$ = \$1/30\$. Which gives 30 days as the answer.

### 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

Mr. X can finish a task in 14 days. Mr. Y can do the same work in 10 days. What is the ratio of the efficiencies of X : Y?

A

\${5/7}\$.

B

\$1{5/7}\$.

C

\${5/6}\$.

D

\${3/4}\$.

Soln.
Ans: a

The efficiency of X is \$100/14\$%, and the efficiency of Y is \$100/10\$%, so the ratio will be \$10/14\$

### Question 5

A, B and C complete a work in 11, 16 and 18 days respectively. All three of them start the work together, but A leaves the work after 1 days, and B leaves the work after 6 days. In how many days will the work be completed?

A

\$9{27/44}\$ days.

B

\$10{27/44}\$ days.

C

\$11{27/44}\$ days.

D

\$12{27/44}\$ 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 = 11, y = 16, z = 18, n = 1, m = 6, and simplifying, we get \${423/44}\$, which is same as: \$9{27/44}\$.