# Time and Work Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time and Work Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. Rakesh, Rohan and Mohan can finish a task in $$10$$ days, $$20$$ days and $$25$$ days respectively. If they start working together, then in how many days they will finish the task?

1. $$4.2 \ days$$
2. $$5.2 \ days$$
3. $$6.5 \ days$$
4. $$8.5 \ days$$

Answer: (b) $$5.2 \ days$$

Solution: Given, $$x = 10$$, $$y = 20$$, $$z = 25$$, then $$= \frac{xyz}{xy + yz + zx}$$ $$= \frac{10 \times 20 \times 25}{10 \times 20 + 20 \times 25 + 25 \times 10}$$ $$= \frac{5000}{200 + 500 + 250}$$ $$= \frac{5000}{950}$$ $$= 5.2 \ days$$

1. Three women K, L and M can finish a work in two days, four days and five days respectively. If they start working together, then in how many days they will finish the work?

1. $$1.05 \ days$$
2. $$2.20 \ days$$
3. $$3.02 \ days$$
4. $$4.06 \ days$$

Answer: (a) $$1.05 \ days$$

Solution: Given, $$x = 2$$, $$y = 4$$, $$z = 5$$, then $$= \frac{xyz}{xy + yz + zx}$$ $$= \frac{2 \times 4 \times 5}{2 \times 4 + 4 \times 5 + 5 \times 2}$$ $$= \frac{40}{38}$$ $$= 1.05 \ days$$

1. P and Q can finish a work in $$5$$ days, Q and R can finish the same work in $$10$$ days and R & P can finish the same work in $$15$$ days. If they start working together, then in how many days they will finish the work?

1. $$6.05 \ days$$
2. $$5.45 \ days$$
3. $$7.58 \ days$$
4. $$8.35 \ days$$

Answer: (b) $$5.45 \ days$$

Solution: Given, $$x = 5$$, $$y = 10$$ and $$z = 15$$ then $$= \frac{2xyz}{xy + yz + zx}$$ $$= \frac{2 \times 5 \times 10 \times 15}{50 + 150 + 75}$$ $$= \frac{1500}{275}$$ $$= 5.45 \ days$$

1. A and B can finish a work in $$8$$ days, B and C can finish the same work in $$10$$ days and C & A can finish the same work in $$12$$ days. If they start working together, then in how many days they will finish the work?

1. $$6.4 \ days$$
2. $$5.4 \ days$$
3. $$7.5 \ days$$
4. $$8.3 \ days$$

Answer: (a) $$6.4 \ days$$

Solution: Given, $$x = 8$$, $$y = 10$$ and $$z = 12$$ then $$= \frac{2xyz}{xy + yz + zx}$$ $$= \frac{2 \times 8 \times 10 \times 12}{80 + 120 + 96}$$ $$= \frac{1920}{296}$$ $$= 6.4 \ days$$

1. A can finish a work in $$5$$ days and B can finish the same work in $$10$$ days. If they work together for $$3$$ days and then A goes away, then in how many more days will B take to finish the work?

1. $$4 \ days$$
2. $$3 \ days$$
3. $$2 \ days$$
4. $$1 \ day$$

Answer: (d) $$1 \ day$$

Solution: Both can finish the part of work in $$3$$ days $$= \left(\frac{1}{5} + \frac{1}{10}\right) \times 3$$ $$= \frac{9}{10}$$ remaining work $$= 1 - \frac{9}{10}$$ $$= \frac{1}{10}$$ then B will finish the remaining work in days $$= \frac{1/10}{1/10}$$ $$= 1 \ day$$

1. P can finish a task in $$10$$ days and Q can finish the same work in $$15$$ days. If they work together for $$5$$ days and then P goes away, then in how many more days will Q take to finish the work?

1. $$4.5 \ days$$
2. $$3.5 \ days$$
3. $$2.5 \ days$$
4. $$1.5 \ days$$

Answer: (c) $$2.5 \ days$$

Solution: Both can finish the part of work in $$5$$ days $$= \left(\frac{1}{10} + \frac{1}{15}\right) \times 5$$ $$= \frac{5}{6}$$ remaining work $$= 1 - \frac{5}{6}$$ $$= \frac{1}{6}$$ then Q will finish the remaining work in days $$= \frac{1/6}{1/15}$$ $$= 2.5 \ days$$

1. $$10$$ Men can finish a work in $$3$$ days, $$8$$ women can finish the same work in $$4$$ days and $$6$$ girls can finish the same work in $$5$$ days. Find in how many days $$1$$ man, $$1$$ women and $$1$$ girl working together can finish the work?

1. $$25.5 \ days$$
2. $$15.3 \ days$$
3. $$12.2 \ days$$
4. $$10.2 \ days$$

Answer: (d) $$10.2 \ days$$

Solution: one man can finish the work in days = $$10 \times 3$$ = $$30$$ days

one women can finish the work in days = $$8 \times 4$$ = $$32$$ days

one girl can finish the work in days = $$6 \times 5$$ = $$30$$ days

then one man, one women and one girl together can finish the part of work in one day $$= \frac{1}{30} + \frac{1}{32} + \frac{1}{30}$$ $$= \frac{94}{960}$$ Hence, one man, one women and one girl together can finish the work $$= \frac{960}{94}$$ $$= 10.2 \ days$$

1. P is three times as efficient as Q and together they can finish a task in $$10$$ days. Find number of days required by Q to finish the same task indivisually?

1. $$39.9 \ days$$
2. $$34.5 \ days$$
3. $$32.6 \ days$$
4. $$30.8 \ days$$

Answer: (a) $$39.9 \ days$$

Solution: Let P requires $$k$$ days to finish the work

and Q requires $$3k$$ days to finish the work, then $$\frac{1}{k} + \frac{1}{3k} = \frac{1}{10}$$ $$k = 13.3 \ days$$ Hence, Q requires $$3k$$ = $$39.9$$ days to finish the work.

1. P can finish a work in $$6$$ days and Q can finish the same work in $$8$$ days, then find how many days are required to finish the work, if both are working together?

1. $$3.4 \ days$$
2. $$5.4 \ days$$
3. $$6.5 \ days$$
4. $$8.6 \ days$$

Answer: (a) $$3.4 \ days$$

Solution: Given, $$x = 6 \ days$$, $$y = 8 \ days$$

If both P and Q start working together then $$= \frac{xy}{x + y}$$ $$= \frac{6 \times 8}{6 + 8}$$ $$= \frac{48}{14}$$ $$= 3.4 \ days$$ Hence, together they can finish the work in $$3.4 \ days$$.

1. A women can finish a work in $$20$$ days, but with the help of her son, she can finish the work in $$10$$ days. Find in how many days her son can finish the work, alone?

1. $$10 \ days$$
2. $$15 \ days$$
3. $$20 \ days$$
4. $$22 \ days$$

Answer: (c) $$20 \ days$$

Solution: together, they can finish the part of work in one day = $$\frac{1}{10}$$

the women alone can finish the part of work in one day = $$\frac{1}{20}$$

then, her son alone can finish the part of work in one day $$= \frac{1}{10} - \frac{1}{20}$$ $$= \frac{1}{20}$$ Hence, her son alone can finish the work in $$20$$ days.