1. Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?

A. 4 hours 20 min B. 5 hours 49 min C. 3 hours 50 min D. 3 hours 22 min

Answer: Option B
Explanation: Part filled by P in 1 hour = [latex]\frac{1}{10 }[/latex] Part filled by Q in 1 hour = [latex]\frac{1}{14 }[/latex] Part filled by (P + Q) in 1 hour = ( [latex]\frac{1}{10 }[/latex] + [latex]\frac{1}{14 }[/latex] ) = ([latex]\frac{6}{35 }[/latex] ) Time taken to fill the tank is ([latex]\frac{35}{6 }[/latex]) = 5 hours 49 min
2. A inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the tank in 16 hours. If both the pipes are opened simultaneously, find the time taken to fill the tank.

A. 36 hours B. 12 hours C. 4 hours D. 48 hours

Answer: Option D
Explanation: As the inlet can fill the tank in 12 hours, in one hour it will fill [latex]\frac{1}{12}[/latex]th of the tank. Similarly, the outlet pipe in one hour can empty [latex]\frac{1}{16 }[/latex] th part of the tank. If both are opened simultaneously, the part of the tank filled in one hour is: [latex]\frac{1}{12 }[/latex] - [latex]\frac{1}{16 }[/latex] = [latex]\frac{1}{48 }[/latex] Hence, the tank gets filled in 48 hours.
3. If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together.

A. 12 minutes B. 20 minutes C. 18 minutes D. 15 minutes

Answer: Option C
Explanation: In 1 minute pipe A can fill [latex]\frac{1}{45 }[/latex]th part of the tank and pipe B can fill [latex]\frac{1}{30 }[/latex]th part of the tank. If they are opened simultaneously then in 1 minute they can fill ([latex]\frac{1}{45 }[/latex] + [latex]\frac{1}{30 }[/latex]) part of the tank = [latex]\frac{1}{18 }[/latex]th part of the tank.
4. If a pipe can fill a tank in 6 hours, find the part of tank it fills in one hour.

A. [latex]\frac{1}{6 }[/latex] B. [latex]\frac{2}{3 }[/latex] C. [latex]\frac{1}{2 }[/latex] D. None of these

Answer: Option C
Explanation: Let the capacity of the tank be C liters. Time to fill the tank = 6 hours Hence, in 1 hour [latex]\frac{C}{6 }[/latex] liters gets filled. Therefore, [latex]\frac{1}{6 }[/latex]th part of the tank gets filled in one hour.
5. A leak at the bottom of the tank can empty the tank in 5 hours, while an inlet pipe can fill the same tank at the rate of 6 litres per minute. When the tank is full, the inlet is opened and the tank gets empty in 8 hours due to the leakage. Find the capacity of the tank.

A. 1800 litres B. 3600 litres C. 4800 litres D. 5760 litres

Answer: Option C
Explanation: The capacity of the tank is given by C = [latex]\frac{(p*q*r)}{(r – p) }[/latex] litres Where, p = time in which the leakage can empty the tank in hours = 5 hours q = rate at which the inlet fills the tank in lph = 6*60 = 360 lph r = time in which the tank gets emptied in hours = 8 hours Hence, C = [latex]\frac{(5*360*8)}{(8 – 5) }[/latex] C = 4800 litres

1. In an examination 80% candidates passed in English and 85% candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what per cent of candidates failed in both the subjects?

A. 8 B. 15 C. 27 D. 35

Answer: Option A
Explanation: Students passed in English = 80% Students passed in Math's = 85% Students passed in both subjects = 73% Then, number of students passed in at least one subject = (80+85)-73 = 92%. [The percentage of students passed in English and Maths individually, have already included the percentage of students passed in both subjects. So, We are subtracting percentage of students who have passed in both subjects to find out percentage of students at least passed in one subject.] Thus, students failed in both subjects = 100-92 = 8%
2. Half percent, written as a decimal, is

A. 0.2 B. 0.02 C. 0.005 D. 0.05

Answer: Option C
Explanation: As we know,1% = [latex]\frac{1}{100 }[/latex] Hence, [latex]\frac{1}{2 }[/latex]% = [latex]\frac{1}{2 }[/latex] X [latex]\frac{1}{100 }[/latex] [latex]\frac{1}{200 }[/latex] = 0.005
3. If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

A. [latex]\frac{1}{4 }[/latex] B. [latex]\frac{1}{3 }[/latex] C. [latex]\frac{1}{2 }[/latex] D. [latex]\frac{2}{3 }[/latex]

Answer: Option B
Explanation: Let the initial price of the commodity be 100. After 50% increase in price, It will become, 100 ------50% increase----> 150. Now, we have to reduce the consumption to keep expenditure 100. Increase in price= 150 - 100 = 50 We have to reduce the consumption, (P + Q)'s 1 day's work = [latex]\frac{50}{150 }[/latex] X 100 [latex]\frac{1}{20 }[/latex] [latex]\frac{1}{3 }[/latex] or 33.33%
4. What will be the fraction of 4%

A. [latex]\frac{1}{20 }[/latex] B. [latex]\frac{1}{50 }[/latex] C. [latex]\frac{1}{75 }[/latex] D. [latex]\frac{1}{25 }[/latex]

Answer: Option D
Explanation: 4* [latex]\frac{1}{100 }[/latex] = [latex]\frac{1}{25 }[/latex]
5. The ratio 5:20 expressed as percent equals to

A. 50 % B. 125 % C. 25 % D. None of above

Answer: Option C
Explanation: Actually it means 5 is what percent of 20, which can be calculated as, [latex]\frac{5}{20 }[/latex]*100 = 5 * 5 = 25

1. 2.09 can be expressed in terms of percentage as

A. 2.09% B. 20.9% C. 209% D. 0.209%

Answer: Option C
Explanation: While calculation in terms of percentage we need to multiply by 100, so 2.09 * 100 = 209.
2. Half of 1 percent written as decimal is

A. 5 B. 0.5 C. 0.05 D. 0.005

Answer: Option D
Explanation: It will be [latex]\frac{1}{2 }[/latex](1%) = [latex]\frac{1}{2 }[/latex]([latex]\frac{1}{100 }[/latex]) = [latex]\frac{1}{200 }[/latex] = 0.005
3. What is 15 percent of 34

A. 5.10 B. 4.10 C. 3.10 D. 2.10

Answer: Option A
Explanation: It will be 15% of 34 = ([latex]\frac{15}{100 }[/latex]) * 34 = 5.10
4. Evaluate 28% of 450 + 45% of 280

A. 232 B. 242 C. 252 D. 262

Answer: Option C
Explanation: = (28/100) * 450 + ([latex]\frac{45}{100 }[/latex]) * 280 = 126 + 126 = 252
5. If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000

10 B. 20 C. 30 D. 40

Answer: Option A
Explanation: Clue: Answer will be 5% of 1000 - 4% of 1000