# Time and Work Quiz Set 012

### Question 1

A can do a work in 4 days. B can destroy the work in 15 days. In how many days will they together complete the work?

A

\$5{5/11}\$ days.

B

\$6{5/11}\$ days.

C

\$7{5/11}\$ days.

D

\$8{5/11}\$ days.

Soln.
Ans: a

Putting x = 4 and y = 15 in the shortcut method, we get \${xy}/{y - x}\$ = \${60/11}\$, which is same as: \$5{5/11}\$.

### Question 2

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 3

A and B can complete a job in 38 and 152 days. They start together but A leaves after working for 30 days. How long would B take to finish the job counting from the day both A and B started together?

A

32 days.

B

33 days.

C

31 days.

D

35 days.

Soln.
Ans: a

If B takes x days. The total job is A's work in 4 days + B's work in x days = \$30/38\$ + \$x/152\$ = 1. Solving, we get x = 32 days.

### Question 4

A can harvest a field in 11 days. B can do the same work in 14 days. In how many days will they together harvest the field?

A

\$6{4/25}\$ days.

B

\$7{4/25}\$ days.

C

\$8{4/25}\$ days.

D

\$9{4/25}\$ days.

Soln.
Ans: a

Putting x = 11 and y = 14 in the shortcut method, we get \${xy}/{x + y}\$ = \${154/25}\$, which is same as: \$6{4/25}\$.

### Question 5

A, B and C can independently complete a work in 19, 9 and 18 days respectively. First C starts the work, then A joined after 5 days, and B after 9 days. In how many days was the work completed?

A

\$10{8/25}\$ days.

B

\$11{8/25}\$ days.

C

\$12{8/25}\$ days.

D

\$13{8/25}\$ 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 = 19, y = 9, z = 18, n = 5, m = 9, and simplifying, we get \${258/25}\$, which is same as: \$10{8/25}\$. 