# Time and Work Quiz Set 018

### Question 1

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

A

4.

B

3.

C

5.

D

6.

Soln.
Ans: a

Since the work force is being doubled proportionately, the time is halved = 4 days.

### Question 2

A, B and C complete a work in 14, 8 and 6 days respectively. All three of them start the work together, but A leaves the work after 6 days, and B leaves the work after 3 days. In how many days will the work be completed?

A

\$1{5/28}\$ days.

B

\$2{5/28}\$ days.

C

\$3{5/28}\$ days.

D

\$4{5/28}\$ 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 = 14, y = 8, z = 6, n = 6, m = 3, and simplifying, we get \${33/28}\$, which is same as: \$1{5/28}\$.

### Question 3

A can harvest a field in 12 days. B can do the same work in 18 days. C can do the same work in 5 days. In how many days will they together harvest the field?

A

\$2{58/61}\$ days.

B

\$3{58/61}\$ days.

C

\$4{58/61}\$ days.

D

\$5{58/61}\$ days.

Soln.
Ans: a

Putting x = 12, y = 18 and z = 5 in the shortcut method, we get \${xyz}/{xy + zy + zx}\$ = \${180/61}\$, which is same as: \$2{58/61}\$.

### Question 4

If 57 men can do a task in 72 days if they work 3 hours per day, how many men are required to complete the task in 19 days if they work 9 hours?

A

72.

B

73.

C

71.

D

75.

Soln.
Ans: a

If m1 men can do a task in d1 days by working h1 hours per day, and m2 in d2 days by working h2 hours per day, then we must have m1 × d1 × h1 = m2 × d2 × h2. Putting m1 = 57, d1 = 72, h1 = 3, d2 = 19, and h2 = 9 we get m2 = 72.

### Question 5

A can do a piece of work in 46 days. B is 15% more efficient than A. In how many days can B complete that work?

A

20 days.

B

21 days.

C

19 days.

D

22 days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/46\$. If B is 15% efficient, then one day work of B is \$1/46\$ × \$115/100\$ = \$1/20\$. Which gives 20 days as the answer. 