# Indian Polity and Constitution

1) A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other ha

- 1) 15 mins
- 2) 20 mins
- 3) 25 mins
- 4) 30 mins

**Ans.**D

**Explanation :**

Let the total time be x mins. Part filled in first half means in x/2 = 1/40 Part filled in second half means in x/2 = \begin{aligned} \frac{1}{60}+\frac{1}{40} \ = \frac{1}{24} \\text{ Total = } \\frac{x}{2}*\frac{1}{40} + \frac{x}{2}*\frac{1}{24} = 1 \ => \frac{x}{2} \left(\frac{1}{40}+\frac{1}{24} \right) = 1 \=> \frac{x}{2}*\frac{1}{15} = 1 \=> x = 30 mins \end{aligned}

2) Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be ful

- 1) 3 hours
- 2) 5 hours
- 3) 7 hours
- 4) 10 hours

**Ans.**B

**Explanation :**

(A+B)'s 2 hour's work when opened = \begin{aligned} \frac{1}{6}+\frac{1}{4} = \frac{5}{12} \ (A+B)'s \text{ 4 hour's work} = \frac{5}{12}*2 \= \frac{5}{6} \text{Remaining work = } 1-\frac{5}{6} \= \frac{1}{6} \ \text{Now, its A turn in 5 th hour} \\frac{1}{6} \text{ work will be done by A in 1 hour}\\text{Total time = }4+1 = 5 hours \end{aligned}

3) A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other ha

- 1) 15 mins
- 2) 20 mins
- 3) 25 mins
- 4) 30 mins

**Ans.**D

**Explanation :**

Let the total time be x mins. Part filled in first half means in x/2 = 1/40 Part filled in second half means in x/2 = \begin{aligned} \frac{1}{60}+\frac{1}{40} \ = \frac{1}{24} \\text{ Total = } \\frac{x}{2}*\frac{1}{40} + \frac{x}{2}*\frac{1}{24} = 1 \ => \frac{x}{2} \left(\frac{1}{40}+\frac{1}{24} \right) = 1 \=> \frac{x}{2}*\frac{1}{15} = 1 \=> x = 30 mins \end{aligned}

4) Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be ful

- 1) 3 hours
- 2) 5 hours
- 3) 7 hours
- 4) 10 hours

**Ans.**B

**Explanation :**

(A+B)'s 2 hour's work when opened = \begin{aligned} \frac{1}{6}+\frac{1}{4} = \frac{5}{12} \ (A+B)'s \text{ 4 hour's work} = \frac{5}{12}*2 \= \frac{5}{6} \text{Remaining work = } 1-\frac{5}{6} \= \frac{1}{6} \ \text{Now, its A turn in 5 th hour} \\frac{1}{6} \text{ work will be done by A in 1 hour}\\text{Total time = }4+1 = 5 hours \end{aligned}

5) Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be ful

- 1) 3 hours
- 2) 5 hours
- 3) 7 hours
- 4) 10 hours

**Ans.**B

**Explanation :**

(A+B)'s 2 hour's work when opened = \begin{aligned} \frac{1}{6}+\frac{1}{4} = \frac{5}{12} \ (A+B)'s \text{ 4 hour's work} = \frac{5}{12}*2 \= \frac{5}{6} \text{Remaining work = } 1-\frac{5}{6} \= \frac{1}{6} \ \text{Now, its A turn in 5 th hour} \\frac{1}{6} \text{ work will be done by A in 1 hour}\\text{Total time = }4+1 = 5 hours \end{aligned}

6) A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other ha

- 1) 15 mins
- 2) 20 mins
- 3) 25 mins
- 4) 30 mins

**Ans.**D

**Explanation :**

Let the total time be x mins. Part filled in first half means in x/2 = 1/40 Part filled in second half means in x/2 = \begin{aligned} \frac{1}{60}+\frac{1}{40} \ = \frac{1}{24} \\text{ Total = } \\frac{x}{2}*\frac{1}{40} + \frac{x}{2}*\frac{1}{24} = 1 \ => \frac{x}{2} \left(\frac{1}{40}+\frac{1}{24} \right) = 1 \=> \frac{x}{2}*\frac{1}{15} = 1 \=> x = 30 mins \end{aligned}

7) A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely

- 1) 2 hours 30 mins
- 2) 2 hours 45 mins
- 3) 3 hours 30 mins
- 4) 3 hours 45 mins

**Ans.**D

**Explanation :**

Half tank will be filled in 3 hours Lets calculate remaining half, Part filled by the four taps in 1 hour = 4*(1/6) = 2/3 Remaining part after 1/2 filled = 1-1/2 = 1/2 \begin{aligned} \frac{2}{3}:\frac{1}{2}::1:X \ => X = \left( \frac{1}{2}*1*{3}{2} \right) \=> X = \frac{3}{4} hrs = 45 \text{ mins} \ \end{aligned} Total time = 3 hours + 45 mins = 3 hours 45 mins

8) A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled

- 1) 7 hours
- 2) 7.1 hours
- 3) 7.2 hours
- 4) 7.3 hours

**Ans.**C

**Explanation :**

When we have question like one is filling the tank and other is empting it, then we subtraction as, Filled in 1 hour = 1/4 Empties in 1 hour = 1/9 Net filled in 1 hour = 1/4 - 1/9 = 5/36 So cistern will be filled in 36/5 hours i.e. 7.2 hours

9) A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely

- 1) 6 min to empty
- 2) 7 min to full
- 3) 6 min to full
- 4) 7 min to empty

**Ans.**A

**Explanation :**

There are two important points to learn in this type of question, First, if both will open then tank will be empty first. Second most important thing is, If we are calculating filling of tank then we will subtract as (filling-empting) If we are calculating empting of thank then we will subtract as (empting-filling) So lets come on the question now, Part to emptied 2/5 Part emptied in 1 minute = \begin{aligned} \frac{1}{6} - \frac{1}{10} \= \frac{1}{15} \=> \frac{1}{15}:\frac{2}{5}::1:x \=> \frac{2}{5}*15 = 6 mins \end{aligned}

10) Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank

- 1) 10 mins
- 2) 12 mins
- 3) 15 mins
- 4) 20 mins

**Ans.**B

**Explanation :**

In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as Part filled by A in 1 min = 1/20 Part filled by B in 1 min = 1/30 Part filled by (A+B) in 1 min = 1/20 + 1/30 = 1/12 So both pipes can fill the tank in 12 mins.