# Time and Work Quiz Set 006

### Question 1

A can do a piece of work in 14 days. B is 40% more efficient than A. In how many days can B complete that work?

A

10 days.

B

11 days.

C

9 days.

D

12 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\$. Which gives 10 days as the answer.

### Question 2

A, B and C can independently complete a work in 5, 15 and 16 days respectively. First C starts the work, then A joined after 7 days, and B after 6 days. In how many days was the work completed?

A

\$8{40/79}\$ days.

B

\$9{40/79}\$ days.

C

\$10{40/79}\$ days.

D

\$11{40/79}\$ 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, and B joins after m days, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x + m/y)\$ days. Putting the various values x = 5, y = 15, z = 16, n = 7, m = 6, and simplifying, we get \${672/79}\$, which is same as: \$8{40/79}\$.

### Question 3

If 30 men can do a task in 54 days if they work 12 hours per day, how many men are required to complete the task in 10 days if they work 9 hours?

A

216.

B

217.

C

215.

D

219.

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 = 30, d1 = 54, h1 = 12, d2 = 10, and h2 = 9 we get m2 = 216.

### Question 4

A can harvest a field in 16 days. B can do the same work in 14 days. C can do the same work in 5 days. In how many days will they together harvest the field?

A

\$2{186/187}\$ days.

B

\$3{186/187}\$ days.

C

\$4{186/187}\$ days.

D

\$5{186/187}\$ days.

Soln.
Ans: a

Putting x = 16, y = 14 and z = 5 in the shortcut method, we get \${xyz}/{xy + zy + zx}\$ = \${560/187}\$, which is same as: \$2{186/187}\$.

### Question 5

If 14 men can do a task in 18 days, how many men are required to complete the task in 7 days?

A

7.

B

8.

C

6.

D

10.

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 = 14, d1 = 18 and d2 = 7, we get m2 = 36.