# Time and Work Quiz Set 001

### Question 1

A, B and C can independently complete a work in 5, 15 and 13 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

\$4{5/67}\$ days.

B

\$5{5/67}\$ days.

C

\$6{5/67}\$ days.

D

\$7{5/67}\$ 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 = 5, y = 15, z = 13, n = 2, and simplifying, we get \${273/67}\$, which is same as: \$4{5/67}\$.

### Question 2

A, B and C complete a work in 6, 4 and 5 days respectively. All three of them start the work together, but A leaves the work after 2 days, and B leaves the work after 1 days. In how many days will the work be completed?

A

\$2{1/12}\$ days.

B

\$3{1/12}\$ days.

C

\$4{1/12}\$ days.

D

\$5{1/12}\$ 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 = 6, y = 4, z = 5, n = 2, m = 1, and simplifying, we get \${25/12}\$, which is same as: \$2{1/12}\$.

### Question 3

A can do a piece of work in 39 days. B is 30% more efficient than A. In how many days will they complete the work if they work together?

A

\$16{22/23}\$ days.

B

17 days.

C

\$17{1/23}\$ days.

D

\$17{2/23}\$ days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/39\$. If B is 30% efficient, then one day work of B is \$1/39\$ × \$130/100\$ = \$1/30\$. Putting x = 39 and y = 30 in the shortcut method, we get \${xy}/{x + y}\$ = \${390/23}\$, which is same as: \$16{22/23}\$.

### Question 4

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 5

If 56 men can do a task in 16 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 = 56, d1 = 16 and d2 = 7, we get m2 = 128.