# Time and Work Quiz Set 017

### Question 1

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 2

If 26 men can do a task in 40 days if they work 9 hours per day, how many men are required to complete the task in 13 days if they work 10 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 = 26, d1 = 40, h1 = 9, d2 = 13, and h2 = 10 we get m2 = 72.

### Question 3

A can do a work in 2 days. B can destroy the work in 7 days. In how many days will they together complete the work?

A

\$2{4/5}\$ days.

B

\$3{4/5}\$ days.

C

\$4{4/5}\$ days.

D

\$5{4/5}\$ days.

Soln.
Ans: a

Putting x = 2 and y = 7 in the shortcut method, we get \${xy}/{y - x}\$ = \${14/5}\$, which is same as: \$2{4/5}\$.

### Question 4

A can harvest a field in 8 days. B can do the same work in 16 days. In how many days will they together harvest the field?

A

\$5{1/3}\$ days.

B

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

C

\$7{1/3}\$ days.

D

\$8{1/3}\$ days.

Soln.
Ans: a

Putting x = 8 and y = 16 in the shortcut method, we get \${xy}/{x + y}\$ = \${16/3}\$, which is same as: \$5{1/3}\$.

### Question 5

A can do a work in 3 days. B can destroy the work in 7 days. In how many days will they together complete the work?

A

\$5{1/4}\$ days.

B

\$6{1/4}\$ days.

C

\$7{1/4}\$ days.

D

\$8{1/4}\$ days.

Soln.
Ans: a

Putting x = 3 and y = 7 in the shortcut method, we get \${xy}/{y - x}\$ = \${21/4}\$, which is same as: \$5{1/4}\$.