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⁞ Percentage

Aptitude ➤ Percentage ➤ 1

1. Concept of Percentage: By a certain percent, we mean that many hundredths.
Thus, x percent means x hundredths, written as x %.

To express x% as a fraction: We have, x % = x/100 .
Thus, 20 % = 20/100 = 1/5 .
To express a/b as a percent: We have, a/b = (a/b) x 100 %.
Thus, 1/4 = (1/4) x 100 % = 25 %.

2. Percentage Increase/Decrease:

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 %

3. Results on Population:
Let the population of a town be P now and suppose it increases at the rate of R % per annum, then:
1. Population after n years = P [1 + (R/100 )]n
2. Population n years ago = P / [1 + (R/100 )]n

4. Results on Depreciation:
Let the present value of a machine be P. Suppose it depreciates at the rate of R % per annum. Then:
1. Value of the machine after n years = P [1 - (R/100 )]n
2. Value of the machine n years ago = P / [1 - (R/100 )]n
3. If A is R % more than B, then B is less than A by [R/(100 + R)] x 100 %.
4. If A is R % less than B, then B is more than A by [R/(100 - R)] x 100 %.

Question 11
Q11.  Rahul requires 40 % to pass. If he gets 185 marks, falls short by 15 marks, what was the maximum he could have got ?
 

Answer :  500


If Rahul has 15 marks more, he could have scored 40 % marks.
Now, 15 marks more than 185 is 185 + 15 = 200.

Let the maximum marks be x,
then, 40 % of x = 200
⇒ (40/100) X x = 200
⇒ x = (200 x 100) / 40 = 500

Thus, maximum marks = 500

Short-Cut / Alternate Method :
Maximum marks = 100(185+15)/40 = (100x200)/40 = 500

♥ The percentage of passing marks in an examination is x %. If a candidate who scores 'y' marks fails by 'z' marks, then the maximum marks,
M = 100(y+z)/x
⚔ DISCUSS

Question 12
Q12.  A candidate scores 15 % and fails by 30 marks, while another candidate who scores 40 % marks, gets 20 marks more than the minimum required marks to pass the examination. Find the maximum marks of the examination.
 

Answer :  200


By Short-Cut Method :

Maximum marks = 100(30+20)/(40-15) = 100x50/25 = 200

♥ A candidate scoring x % and fails by 'a' marks, while another candidate who scores y % marks, gets 'b' marks more than the minimum required passing marks. Then the maximum marks M = 100(a+b)/(y-x)
⚔ DISCUSS

Question 13
Q13.  In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
 

Answer :  2700


Number of valid votes = 80 % of 7500 = 6000.
∴ Valid votes polled by other candidate = 45 % of 6000
= (45/100) x 6000 = 2700.
⚔ DISCUSS

Question 14
Q14.  Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items ?
 

Answer :  Rs. 19.70


Let the amount taxable purchases be Rs. x.
Then, 6 % of x = 30/100
⇒ x = (30/100) x (100/6) = 5.

∴ Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
⚔ DISCUSS

Question 15
Q15.  Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week ?
 

Answer :  Rs. 250


Let the sum paid to Y per week be Rs. z.
Then, z + 120 % of z = 550.
⇒ z + (120/100) z = 550
⇒ (11/5) z = 550
⇒ z = (550 x 5)/11 = 250.
⚔ DISCUSS

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