# Time and Work Quiz Set 004

### Question 1

If 102 men can do a task in 48 days if they work 17 hours per day, how many men are required to complete the task in 17 days if they work 16 hours?

A

306.

B

307.

C

305.

D

309.

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 = 102, d1 = 48, h1 = 17, d2 = 17, and h2 = 16 we get m2 = 306.

### Question 2

A can harvest a field in 19 days. B can do the same work in 4 days. C can do the same work in 10 days. In how many days will they together harvest the field?

A

\$2{74/153}\$ days.

B

\$3{74/153}\$ days.

C

\$4{74/153}\$ days.

D

\$5{74/153}\$ days.

Soln.
Ans: a

Putting x = 19, y = 4 and z = 10 in the shortcut method, we get \${xyz}/{xy + zy + zx}\$ = \${380/153}\$, which is same as: \$2{74/153}\$.

### Question 3

A can harvest a field in 2 days. B can do the same work in 9 days. In how many days will they together harvest the field?

A

\$1{7/11}\$ days.

B

\$2{7/11}\$ days.

C

\$3{7/11}\$ days.

D

\$4{7/11}\$ days.

Soln.
Ans: a

Putting x = 2 and y = 9 in the shortcut method, we get \${xy}/{x + y}\$ = \${18/11}\$, which is same as: \$1{7/11}\$.

### Question 4

A can harvest a field in 19 days. B can do the same work in 13 days. C can do the same work in 5 days. How much did A get if the farmer pays them a total amount of Rs. 13300 for a work that they together completed in 4 days?

A

Rs. 2800.

B

Rs. 2900.

C

Rs. 2700.

D

Rs. 3100.

Soln.
Ans: a

Work done by A in 1 day = \$1/19\$. So the work in 4 days = 4 × \$1/19\$. His share is Rs. 4 × \$1/19\$ × 13300 = Rs. 2800.

### Question 5

A can do a work in 4 days. B can destroy the work in 15 days. In how many days will they together complete the work?

A

\$5{5/11}\$ days.

B

\$6{5/11}\$ days.

C

\$7{5/11}\$ days.

D

\$8{5/11}\$ days.

Soln.
Ans: a

Putting x = 4 and y = 15 in the shortcut method, we get \${xy}/{y - x}\$ = \${60/11}\$, which is same as: \$5{5/11}\$.