# Time and Work Quiz Set 016

### Question 1

A, B and C can independently complete a work in 17, 18 and 4 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{15/223}\$ days.

B

\$4{15/223}\$ days.

C

\$5{15/223}\$ days.

D

\$6{15/223}\$ 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 = 17, y = 18, z = 4, n = 2, and simplifying, we get \${684/223}\$, which is same as: \$3{15/223}\$.

### Question 2

A and B can together complete a job in 16 days. A can alone complete it in 24 days. How long would B alone take to finish the job?

A

48 days.

B

49 days.

C

47 days.

D

51 days.

Soln.
Ans: a

One day work of A + B is \$1/16\$. One day work of A is \$1/24\$. So one day work of B, say, \$1/y\$ = \$1/16\$ - \$1/24\$. Solving, we get y = 48 days.

### Question 3

Mr. P is thrice as efficient as Mr. Q and can finish a piece of work by taking 12 days less. In how many days does Mr. P finish that work?

A

6.

B

5.

C

7.

D

8.

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 = 12. Solving, x = 6.

### Question 4

A, B and C complete a work in 8, 18 and 19 days respectively. All three of them start the work together, but A leaves the work after 3 days. In how many days will the work be completed?

A

\$5{115/148}\$ days.

B

\$6{115/148}\$ days.

C

\$7{115/148}\$ days.

D

\$8{115/148}\$ 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 = 8, y = 18, z = 19, n = 3, and simplifying, we get \${855/148}\$, which is same as: \$5{115/148}\$.

### Question 5

A, B and C complete a work in 19, 9 and 11 days respectively. All three of them start the work together, but A leaves the work after 5 days. In how many days will the work be completed?

A

\$3{123/190}\$ days.

B

\$4{123/190}\$ days.

C

\$5{123/190}\$ days.

D

\$6{123/190}\$ 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 = 9, z = 11, n = 5, and simplifying, we get \${693/190}\$, which is same as: \$3{123/190}\$.