## Tutorials to solve Percentage’s Questions in Aptitude

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% = z100
pq as percent: (pq 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 + R100)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 – R100)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’sQuestion with solved example:

Q1. What is fraction equivalent of 32%.

[A] 6/30
[B] 8/25
[C] 7/50
[D] 11:10

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

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

Explanation

`0.8% = 0.8/100 = 0.008.`

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

[A] 352
[B] 252
[C] 452
[D] 552

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%

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 4/5th of that number. Find the number.

[A] 140
[B] 130
[C] 120
[D] 110

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%

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

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

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

```Population after 2 years =  {176400 * (1+5/100)2 }