# Time and Work Quiz Set 019

### Question 1

6 men and 4 women finish a job in 32 days. In how many days will 8 women and 12 men finish that job?

A

16.

B

15.

C

17.

D

18.

Soln.
Ans: a

Since the work force is being doubled proportionately, the time is halved = 16 days.

### Question 2

A can do a piece of work in 14 days. B is 40% more efficient than A. In how many days will they complete the work if they work together?

A

\$5{5/6}\$ days.

B

6 days.

C

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

D

\$6{1/3}\$ days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/14\$. If B is 40% efficient, then one day work of B is \$1/14\$ × \$140/100\$ = \$1/10\$. Putting x = 14 and y = 10 in the shortcut method, we get \${xy}/{x + y}\$ = \${35/6}\$, which is same as: \$5{5/6}\$.

### Question 3

A and B can together complete a job in 21 days. A can alone complete it in 28 days. How long would B alone take to finish the job?

A

84 days.

B

85 days.

C

83 days.

D

87 days.

Soln.
Ans: a

One day work of A + B is \$1/21\$. One day work of A is \$1/28\$. So one day work of B, say, \$1/y\$ = \$1/21\$ - \$1/28\$. Solving, we get y = 84 days.

### Question 4

A, B and C can independently complete a work in 18, 16 and 6 days respectively. B and C start the work together, but A joins them after 2 days. In how many days will the work be completed?

A

\$3{37/41}\$ days.

B

\$4{37/41}\$ days.

C

\$5{37/41}\$ days.

D

\$6{37/41}\$ 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 = 18, y = 16, z = 6, n = 2, and simplifying, we get \${160/41}\$, which is same as: \$3{37/41}\$.

### Question 5

Mr. P is thrice as efficient as Mr. Q and can finish a piece of work by taking 10 days less. In how many days does Mr. P finish that work?

A

5.

B

4.

C

6.

D

7.

Soln.
Ans: a

Let the time taken by P be x days. Then the time taken by Q is 3x. The difference is 3x - x. So, 2x = 10. Solving, x = 5.