Tutorials to solve Percentages Questions in Aptitude

## Percentage

Percent means many hundredths. Example: z% is z percent which means z hundredths. It will be written as:

z% = ^{z}⁄_{100}^{p}⁄_{q} as percent: (^{p}⁄_{q} x 100)%

## Commodity

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

[^{R}⁄_{(100 + R)}x 100]%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

[^{R}⁄_{(100 – R)}x 100]%

## Population

The population of a city is P and let it increases at the rate of R% per annum:

- Population after t years: P(1 +
^{R}⁄_{100})^{t} - Population t years ago:
^{P}⁄_{(1 + R⁄100)t}

## Depreciation

Let V be the present value of machine. Suppose it depreciates at the rate of R% per annum:

- Machine’s value after t years:P(1 –
^{R}⁄_{100})^{t} - Machine’s value t years ago:
^{P}⁄_{(1 – R⁄100)t}

**If P is R% more than Q, then Q is less than P by how many percent?**

[^{R}⁄_{(100 + R)}x 100]%

**If P is R% more than Q, then Q is more than P by how many percent?**

[^{R}⁄_{(100 – R)}x 100]%

**Percentage’s** **Question with solved example:**

**Q1. What is fraction equivalent of 32%.**

[A] 6/30

[B] 8/25

[C] 7/50

[D] 11:10

**Answer – B**

**Explanation**:

32% = 32/100 = 8/25.

**Q2. What is fraction equivalent of 160%.**

[A] 8/5

[B] 9/5

[C] 6/7

[D] 6/23

**Answer – A**

**Explanation**

160% = 160/100 = 8/5

**Q3. What is decimal equivalent of 0.8%.**

[A] 0.008

[B] 0.08

[C] 0.8

[D] 0.0008

**Answer – A**

**Explanation**

0.8% = 0.8/100 = 0.008.

**Q4. 45% of 280 + 28% of 450 = ?.**

[A] 352

[B] 252

[C] 452

[D] 552

**Answer – B**

**Explanation**

45% of 280+28% of 450 = (450/100*280)(28/100*450) = (126+126) = 252

**Q5. Which is largest in 50/3%, 2/15, 0.18, 3/7 ?**

[A] 0.18

[B] 3/7

[C] 2/15

[D] 50/3%

**Answer – B**

**Explanation**

162/3% = 50/(3*100) = 1/6 = 0.166, 2/15 =0.133, 3rd number = 0.18, 3/7 = 0.42. Clearly, 3/7 is largest.

**Q6. 65% of a number is 21 less than 4/5 ^{th} of that number. Find the number.**

[A] 140

[B] 130

[C] 120

[D] 110

**Answer – A**

**Explanation**

Let the number be x. Then, (4/5 x)-(65% of x)= 21 => 4x/5-65x/100=21 => 4x/5-13x/20=21 => 16x-13x=420 =>3x=420 ?x=140. Required number = 140.

**Q7. If A’s pay is 20% more than that of B, then what number of per penny is B’s compensation not as much as that of A?**

[A] 50/3%

[B] 60/3%

[C] 70/3%

[D] 80/3%

**Answer – A**

**Explanation**

B's salary is less than that of A by is less than that of a by {R/((100+R) )*100}% = {20/((120) )*100}% = 50/3%

**Q8. If the cost of sugar falls by 10%, by how much per penny should a householder expand its utilization, so as not to diminish its use on sugar?**

[A] 100/9

[B] 10/9

[C] 100/3

[D] 10/3

**Answer – A**

**Explanation**

Increase % in consumption = {R/((100-R) )*100}% = {10/((100-10) )*100} = 100/9%

**Q9. The tax on a commodity is diminished by 20% and its consumption increases by 15%. Find the effect on revenue.**

[A] 8% increase

[B] 8% decrease

[C] 10% increase

[D] 10% increase

**Answer – B**

**Explanation**

Let originally revenue obtained by Rs. x. New revenue = (Consumption * Tax) = (115% of 80% of Rs. x) = Rs(115/100*80/100*x)=Rs.92x/100 = 92% of the original. Hence, the revenue is decreased by 8%.

**Q10. The population of a town is 176400. It increases annually at the rate of 5% p.a. What will be its population after 2 years?**

[A] 194481

[B] 294481

[C] 394481

[D] 494481

**Answer – A**

**Explanation**

Population after 2 years = {176400 * (1+5/100)2 } 176400* 21/20*21/20=194481.

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