# Time and Work Quiz Set 016

### Question 1

A can do a piece of work in 39 days. B is 30% more efficient than A. In how many days can B complete that work?

A

30 days.

B

31 days.

C

29 days.

D

32 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\$. Which gives 30 days as the answer.

### Question 2

A and B can together complete a job in 12 days. A can alone complete it in 14 days. How long would B alone take to finish the job?

A

84 days.

B

85 days.

C

83 days.

D

87 days.

Soln.
Ans: a

One day work of A + B is \$1/12\$. One day work of A is \$1/14\$. So one day work of B, say, \$1/y\$ = \$1/12\$ - \$1/14\$. Solving, we get y = 84 days.

### Question 3

A can harvest a field in 12 days. B can do the same work in 7 days. In how many days will they together harvest the field?

A

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

B

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

C

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

D

\$7{8/19}\$ days.

Soln.
Ans: a

Putting x = 12 and y = 7 in the shortcut method, we get \${xy}/{x + y}\$ = \${84/19}\$, which is same as: \$4{8/19}\$.

### Question 4

A, B and C can independently complete a work in 16, 11 and 6 days respectively. First C starts the work, then A joined after 3 days, and B after 2 days. In how many days was the work completed?

A

\$4{47/169}\$ days.

B

\$5{47/169}\$ days.

C

\$6{47/169}\$ days.

D

\$7{47/169}\$ 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 = 16, y = 11, z = 6, n = 3, m = 2, and simplifying, we get \${723/169}\$, which is same as: \$4{47/169}\$.

### Question 5

If 102 men can do a task in 48 days if they work 17 hours per day, how many men are required to complete the task in 17 days if they work 16 hours?

A

306.

B

307.

C

305.

D

309.

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 = 102, d1 = 48, h1 = 17, d2 = 17, and h2 = 16 we get m2 = 306. 