# 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. A pipe can fill the tank in $$10$$ hours and pipe B can empty the tank in $$15$$ hours. Find the time required to fill the tank, if both pipes are running simultaneously?

1. $$10 \ hours$$
2. $$20 \ hours$$
3. $$30 \ hours$$
4. $$40 \ hours$$

Answer: (c) $$30 \ hours$$

Solution: Part of the tank filled in one hour $$= \frac{1}{10} - \frac{1}{15}$$ $$= \frac{1}{30}$$ Hence, the tank will be filled in $$30$$ hours

1. A cistern is normally filled in $$10$$ hours, but it takes $$12$$ hours, when there is a leak in its bottom. If cistern is full, in what time shall the leak empty the cistern?

1. $$30 \ hours$$
2. $$40 \ hours$$
3. $$50 \ hours$$
4. $$60 \ hours$$

Answer: (d) $$60 \ hours$$

Solution: Let leak can empty the cistern in $$x$$ hours, then $$\frac{1}{10} - \frac{1}{x} = \frac{1}{12}$$ $$\frac{1}{10} - \frac{1}{12} = \frac{1}{x}$$ $$\frac{1}{60} = \frac{1}{x}$$ Hence, leak can empty the tank in $$60$$ hours.

1. If pipe M can fill the tank in $$6$$ hours and pipe N can empty the tank in $$8$$ hours, then find how many hours will it take to fill a half empty tank?

1. $$10 \ hours$$
2. $$12 \ hours$$
3. $$15 \ hours$$
4. $$18 \ hours$$

Answer: (b) $$12 \ hours$$

Solution: part of the tank filled in one hour $$= \frac{1}{6} - \frac{1}{8}$$ $$= \frac{1}{24}$$ Hence, full tank will be filled in $$24$$ hours and half tank will be filled in $$12$$ hours.

1. Two taps P and Q can fill a tank in $$5$$ hours and $$10$$ hours, respectively. If both taps are opened together, then find the time required to fill the tank?

1. $$\frac{10}{3} \ hours$$
2. $$\frac{3}{10} \ hours$$
3. $$\frac{12}{5} \ hours$$
4. $$\frac{5}{12} \ hours$$

Answer: (a) $$\frac{10}{3} \ hours$$

Solution: net part of the tank filled in one hour $$= \frac{1}{5} + \frac{1}{10}$$ $$= \frac{3}{10}$$ Hence, tank will be filled in $$\frac{10}{3}$$ hours.

1. One tap can fill a tank in $$5$$ hours and another tap can empty the tank in $$6$$ hours. How long will they take to fill the tank, if both the taps are opened?

1. $$10 \ hours$$
2. $$20 \ hours$$
3. $$30 \ hours$$
4. $$40 \ hours$$

Answer: (c) $$30 \ hours$$

Solution: net part of the tank filled in one hour $$= \frac{1}{5} - \frac{1}{6}$$ $$= \frac{1}{30}$$ Hence, tank will be filled in $$30$$ hours.

1. Two inlet pipes can fill the tank in $$5$$ hours and $$10$$ hours respectively, while two outlet pipes can empty the full tank in $$15$$ and $$20$$ hours, respectively. If pipes are running simultaneously, then find the time required to fill the tank?

1. $$\frac{60}{11} \ hours$$
2. $$\frac{11}{60} \ hours$$
3. $$\frac{65}{12} \ hours$$
4. $$\frac{12}{65} \ hours$$

Answer: (a) $$\frac{60}{11} \ hours$$

Solution: Given, $$x_1 = 5$$, $$x_2 = 10$$, $$y_1 = 15$$ and $$y_2 = 20$$

then net part of the tank filled in one hour $$= \left(\frac{1}{5} + \frac{1}{10}\right) - \left(\frac{1}{15} + \frac{1}{20}\right)$$ $$= \frac{3}{10} - \frac{7}{60}$$ $$= \frac{11}{60}$$ Hence, the tank will be filled in $$\frac{60}{11}$$ hours.

1. A cistern is normally filled in $$12$$ hours but takes $$3$$ hours more to fill because of a leak in its bottom. If the cistern is full, then how many hours the leak will take to empty the tank?

1. $$30 \ hours$$
2. $$40 \ hours$$
3. $$50 \ hours$$
4. $$60 \ hours$$

Answer: (d) $$60 \ hours$$

Solution: Let the leak can empty the tank in $$x$$ hours, then $$\frac{1}{12} - \frac{1}{x} = \frac{1}{15}$$ $$= \frac{1}{12} - \frac{1}{15} = \frac{1}{x}$$ $$\frac{1}{60} = \frac{1}{x}$$ $$x = 60 \ hours$$

1. Two pipes can fill a tank in $$4$$ hours and $$6$$ hours respectively, while a third pipe empties the full tank in $$10$$ hours. If all the three pipes operate simultaneously, then how much time it will take to fill the tank?

1. $$2.5 \ hours$$
2. $$3.1 \ hours$$
3. $$4.2 \ hours$$
4. $$5.3 \ hours$$

Answer: (b) $$3.1 \ hours$$

Solution: part of the tank filled in one hour $$= \frac{1}{4} + \frac{1}{6} - \frac{1}{10}$$ $$= \frac{19}{60}$$ Hence, the tank will be filled in $$\frac{60}{19}$$ hours or $$3.1$$ hours.

1. One tap can fill a tank in $$6$$ hours and another tap can empty the tank in $$8$$ hours. How long will they take to fill the tank, if both the taps are opened?

1. $$20 \ hours$$
2. $$21 \ hours$$
3. $$23 \ hours$$
4. $$24 \ hours$$

Answer: (d) $$24 \ hours$$

Solution: net part of the tank filled in one hour $$= \frac{1}{6} - \frac{1}{8}$$ $$= \frac{1}{24}$$ Hence, tank will be filled in $$24$$ hours.

1. Two taps A and B can fill a tank in $$2$$ hours and $$4$$ hours, respectively. If both taps are opened together, then find the time required to fill the tank?

1. $$\frac{3}{4} \ hours$$
2. $$\frac{4}{3} \ hours$$
3. $$\frac{5}{2} \ hours$$
4. $$\frac{2}{5} \ hours$$

Answer: (b) $$\frac{4}{3}$$

Solution: net part of the tank filled in one hour $$= \frac{1}{2} + \frac{1}{4}$$ $$= \frac{3}{4}$$ Hence, tank will be filled in $$\frac{4}{3}$$ hours.