Percentage (āĻļāĻ¤āĻžāĻāĻļ) â Top 30 Standard Questions for Competitive Exams
Q / āĻĒā§ā§°āĻļā§āĻ¨-1: If A's income is 25% morethan B's income, then B's income is what percent less than A's income ? (āĻ¯āĻĻāĻŋ A-ā§° āĻā§, B-ā§° āĻā§āĻ¤āĻā§ 25% āĻŦā§āĻāĻŋ āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ B-ā§° āĻā§, A-ā§° āĻā§āĻ¤āĻā§ āĻāĻŋāĻŽāĻžāĻ¨ āĻļāĻ¤āĻžāĻāĻļ āĻāĻŽ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 20% | B) 25% | C) 16â % | D) 33â %
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Assume B's income (āĻ§ā§°āĻž āĻ¯āĻžāĻāĻ, B-ā§° āĻā§) = âš100
Percentage less (āĻļāĻ¤āĻžāĻāĻļ āĻāĻŽ): 25/125 × 100 = 20%
Ans / āĻāĻ¤ā§āĻ¤ā§°: A) 20%
Shortcut: If A is x% more than B, then B is less than A by (āĻ¯āĻĻāĻŋ A, B-āĻ¤āĻā§ x% āĻŦā§āĻāĻŋ āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ B, A-āĻ¤āĻā§ āĻāĻŽ āĻš'āĻŦ)
x / 100 + x × 100
Here / āĻāĻ¯āĻŧāĻžāĻ¤,
x = 25
25/100 x 100 =20%
Ans / āĻāĻ¤ā§āĻ¤ā§°: A) 20%
Q / āĻĒā§ā§°āĻļā§āĻ¨ ā§¨ : A number, when 60 is subtracted from 60% of it, gives 60 as the result. Find the number.(āĻāĻāĻž āĻ¸āĻāĻā§āĻ¯āĻžā§° 60% ā§° āĻĒā§°āĻž 60 āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻŋāĻ˛ā§, āĻŦāĻŋāĻ¯āĻŧā§āĻāĻĢāĻ˛ 60 āĻšāĻ¯āĻŧāĨ¤ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻžāĨ¤)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 120 | B) 150 | C) 180 | D) 200
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Let the number be x. ((āĻ§ā§°āĻž āĻ¯āĻžāĻāĻ, āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ xāĨ¤)
According to the question: āĻĒā§ā§°āĻļā§āĻ¨ āĻ āĻ¨ā§āĻ¸ā§°āĻŋ,
60% of x − 60 = 60
60x / 100 = 60 + 60
60x / 100 = 120
60x = 120 × 100
x = 120 × 100 / 60
x = 200
Ans / āĻāĻ¤ā§āĻ¤ā§°: D) 200
Shortcut: 60% of Number = 60 + 60 = 120
60% = 120
100% = 120 × 100 / 60 = 200
Ans / āĻāĻ¤ā§āĻ¤ā§°: D) 200
Q3/āĻĒā§ā§°āĻļā§āĻ¨ ā§Š: Due to a 20% increase in the price of sugar, by what percentage should a family reduce its sugar consumption so that the expenditure on sugar remains unchanged ? (āĻāĻŋāĻ¨āĻŋā§° āĻŽā§āĻ˛ā§āĻ¯ 20% āĻŦā§āĻĻā§āĻ§āĻŋ āĻĒā§ā§ąāĻžā§° āĻĢāĻ˛āĻ¤, āĻāĻŋāĻ¨āĻŋā§° āĻŦāĻžāĻŦāĻĻ āĻā§°āĻ āĻāĻā§ ā§°āĻžāĻāĻŋāĻŦāĻ˛ā§ āĻāĻāĻž āĻĒā§°āĻŋāĻ¯āĻŧāĻžāĻ˛ā§ āĻāĻŋāĻ¨āĻŋā§° āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻāĻŋāĻŽāĻžāĻ¨ āĻļāĻ¤āĻžāĻāĻļ āĻāĻŽāĻžāĻŦ āĻ˛āĻžāĻāĻŋāĻŦ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 20% | B) 16â % | C) 25% | D) 15%
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
When the price increases, consumption must decrease to keep expenditure unchanged. (āĻŽā§āĻ˛ā§āĻ¯ āĻŦā§āĻĻā§āĻ§āĻŋ āĻĒāĻžāĻ˛ā§, āĻā§°āĻ āĻāĻā§ ā§°āĻžāĻāĻŋāĻŦāĻ˛ā§ āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻāĻŽāĻžāĻŦ āĻ˛āĻžāĻā§āĨ¤)
Formula / āĻ¸ā§āĻ¤ā§ā§°: Reduction % = R/(100+R) × 100
where (āĻāĻ¯āĻŧāĻžāĻ¤) R = Percentage Increase in Price ( āĻŽā§āĻ˛ā§āĻ¯ āĻŦā§āĻĻā§āĻ§āĻŋā§° āĻļāĻ¤āĻžāĻāĻļ)
= 20/(100 + 20) × 100 = 20/120 × 100 = 16â %
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 16â %Shortcut:
If the price increases by R%, then the required reduction in consumption is: (āĻ¯āĻĻāĻŋ āĻŽā§āĻ˛ā§āĻ¯ R% āĻŦā§āĻĻā§āĻ§āĻŋ āĻĒāĻžāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻāĻŽāĻžāĻŦ āĻ˛āĻžāĻāĻŋāĻŦ:)
R / (100+R) × 100
For / R = 20%
20/120 × 100 = 6â %
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 16â %
Q 4 / āĻĒā§ā§°āĻļā§āĻ¨ ā§Ē: If the length of a rectangle is increased by 20% and its breadth is decreased by 10%, what will be the change in its area? āĻ¯āĻĻāĻŋ āĻāĻāĻž āĻāĻ¯āĻŧāĻ¤āĻā§āĻˇā§āĻ¤ā§ā§°ā§° āĻĻā§ā§°ā§āĻā§āĻ¯ 20% āĻŦā§āĻĻā§āĻ§āĻŋ āĻā§°āĻž āĻšāĻ¯āĻŧ āĻā§°ā§ āĻĒā§ā§°āĻ¸ā§āĻĨ 10% āĻšā§ā§°āĻžāĻ¸ āĻā§°āĻž āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ āĻāĻ¯āĻŧāĻžā§° āĻā§āĻˇā§āĻ¤ā§ā§°āĻĢāĻ˛āĻ¤ āĻāĻŋ āĻĒā§°āĻŋāĻŦāĻ°ā§āĻ¤āĻ¨ āĻš'āĻŦ?
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 10% Increase (āĻŦā§āĻĻā§āĻ§āĻŋ)B) 8% Increase (āĻŦā§āĻĻā§āĻ§āĻŋ) C) 10% Decrease (āĻšā§ā§°āĻžāĻ¸) D) 8% Decrease (āĻšā§ā§°āĻžāĻ¸)
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Using the Successive Percentage Change Formula:
Successive Change = x + y + xy/100â
Here / āĻāĻ¯āĻŧāĻžāĻ¤, x = +20, y= −10 x = +20,
= 20 - 10 + { 20×(−10)}/100â=10 - 2 = 8%
Since the result is positive, the area increases. (āĻĢāĻ˛āĻžāĻĢāĻ˛ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻšā§ā§ąāĻž āĻŦāĻžāĻŦā§ āĻā§āĻˇā§āĻ¤ā§ā§°āĻĢāĻ˛ āĻŦā§āĻĻā§āĻ§āĻŋ āĻĒāĻžāĻ¯āĻŧāĨ¤)
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 8% Increase (āĻŦā§āĻĻā§āĻ§āĻŋ)