# Time and Work Quiz Set 002

### Question 1

Mr. P is thrice as efficient as Mr. Q and can finish a piece of work by taking 24 days less. In how many days does Mr. P finish that work?

A

12.

B

11.

C

13.

D

14.

Soln.
Ans: a

Let the time taken by P be x days. Then the time taken by Q is 3x. The difference is 3x - x. So, 2x = 24. Solving, x = 12.

### Question 2

A, B and C can independently complete a work in 18, 11 and 13 days respectively. First C starts the work, then A joined after 4 days, and B after 1 days. In how many days was the work completed?

A

\$5{101/115}\$ days.

B

\$6{101/115}\$ days.

C

\$7{101/115}\$ days.

D

\$8{101/115}\$ 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 = 18, y = 11, z = 13, n = 4, m = 1, and simplifying, we get \${676/115}\$, which is same as: \$5{101/115}\$.

### Question 3

A can do a piece of work in 18 days. B is 20% more efficient than A. In how many days can B complete that work?

A

15 days.

B

16 days.

C

14 days.

D

17 days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/18\$. If B is 20% efficient, then one day work of B is \$1/18\$ × \$120/100\$ = \$1/15\$. Which gives 15 days as the answer.

### Question 4

A, B and C complete a work in 9, 16 and 19 days respectively. All three of them start the work together, but A leaves the work after 1 days, and B leaves the work after 7 days. In how many days will the work be completed?

A

\$8{83/144}\$ days.

B

\$9{83/144}\$ days.

C

\$10{83/144}\$ days.

D

\$11{83/144}\$ 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 = 9, y = 16, z = 19, n = 1, m = 7, and simplifying, we get \${1235/144}\$, which is same as: \$8{83/144}\$.

### Question 5

A, B and C complete a work in 19, 14 and 7 days respectively. All three of them start the work together, but A leaves the work after 1 days. In how many days will the work be completed?

A

\$4{8/19}\$ days.

B

\$5{8/19}\$ days.

C

\$6{8/19}\$ days.

D

\$7{8/19}\$ 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, the work is completed in \${yz}/{y + z}\$ × \$(1 - n/x)\$ days. Putting the various values x = 19, y = 14, z = 7, n = 1, and simplifying, we get \${84/19}\$, which is same as: \$4{8/19}\$.