# Time and Work Quiz Set 005

### Question 1

If 26 men can do a task in 40 days if they work 9 hours per day, how many men are required to complete the task in 13 days if they work 10 hours?

A

72.

B

73.

C

71.

D

75.

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 = 26, d1 = 40, h1 = 9, d2 = 13, and h2 = 10 we get m2 = 72.

### Question 2

A can harvest a field in 14 days. B can do the same work in 16 days. C can do the same work in 7 days. In how many days will they together harvest the field?

A

\$3{19/31}\$ days.

B

\$4{19/31}\$ days.

C

\$5{19/31}\$ days.

D

\$6{19/31}\$ days.

Soln.
Ans: a

Putting x = 14, y = 16 and z = 7 in the shortcut method, we get \${xyz}/{xy + zy + zx}\$ = \${112/31}\$, which is same as: \$3{19/31}\$.

### Question 3

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 4

A, B and C can independently complete a work in 17, 18 and 19 days respectively. B and C start the work together, but A joins them after 3 days. In how many days will the work be completed?

A

\$7{43/971}\$ days.

B

\$8{43/971}\$ days.

C

\$9{43/971}\$ days.

D

\$10{43/971}\$ 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 = 19, n = 3, and simplifying, we get \${6840/971}\$, which is same as: \$7{43/971}\$.

### Question 5

A and B can complete a job in 24 and 72 days. They start together but A leaves after working for 10 days. How long would B take to finish the job counting from the day both A and B started together?

A

42 days.

B

43 days.

C

41 days.

D

45 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 = \$10/24\$ + \$x/72\$ = 1. Solving, we get x = 42 days. 