# Time and Work Quiz Set 003

### Question 1

A can finish a work in 5 days. B can do the same work in 7 days. They work together for 2 days. The fraction of work that is left is?

A

\${11/35}\$.

B

\$1{11/35}\$.

C

\${11/34}\$.

D

\${1/3}\$.

Soln.
Ans: a

They together finish \$1/5 + 1/7\$ work in a day. In 2 days they finish 2 × \$(1/5 + 1/7)\$ work, which is \$24/35\$. So the un-finished work is 1 - \$24/35\$ = \${11/35}\$.

### Question 2

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 3

A can do a piece of work in 39 days. B is 30% more efficient than A. In how many days will they complete the work if they work together?

A

\$16{22/23}\$ days.

B

17 days.

C

\$17{1/23}\$ days.

D

\$17{2/23}\$ 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\$. Putting x = 39 and y = 30 in the shortcut method, we get \${xy}/{x + y}\$ = \${390/23}\$, which is same as: \$16{22/23}\$.

### Question 4

If 70 men can do a task in 17 days, how many men are required to complete the task in 14 days?

A

85.

B

15.

C

13.

D

17.

Soln.
Ans: a

If m1 men can do a task in d1 days, and m2 in d2, then we must have m1 × d1 = m2 × d2. Putting m1 = 70, d1 = 17 and d2 = 14, we get m2 = 85.

### Question 5

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}\$.