Percentage (āĻļāϤāĻžāĻ‚āĻļ) – Top 30 Standard Questions for Competitive Exams













Q / āĻĒā§ā§°āĻļā§āύ-1If A's income is 25% more than B's income, then B's income is what percent less than A's income ? (āϝāĻĻāĻŋ A-ā§° āĻ†ā§Ÿ, B-ā§° āĻ†ā§ŸāϤāĻ•ā§ˆ 25% āĻŦ⧇āĻ›āĻŋ āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ B-ā§° āĻ†ā§Ÿ, A-ā§° āĻ†ā§ŸāϤāĻ•ā§ˆ āĻ•āĻŋāĻŽāĻžāύ āĻļāϤāĻžāĻ‚āĻļ āĻ•āĻŽ ?)


Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš: A) 20% | B) 25% | C) 16⅔% | D) 33⅓%


Soln / āϏāĻŽāĻžāϧāĻžāύ

  • Assume B's income (āϧ⧰āĻž āϝāĻžāĻ“āĻ•, B-ā§° āĻ†ā§Ÿ) = ₹100

  • A's income (A-ā§° āĻ†ā§Ÿ) = 100 + 25 = ₹125

  • Difference (āĻĒāĻžā§°ā§āĻĨāĻ•ā§āϝ) = 125 − 100 = ₹25

  • Percentage less (āĻļāϤāĻžāĻ‚āĻļ āĻ•āĻŽ): 25/125 × 100 = 20%


Ans / āωāĻ¤ā§āϤ⧰: A) 20%


Shortcut: If A is x% more than B, then B is less than A by (āϝāĻĻāĻŋ A, B-āϤāĻ•ā§ˆ x% āĻŦ⧇āĻ›āĻŋ āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ B, A-āϤāĻ•ā§ˆ āĻ•āĻŽ āĻš'āĻŦ)

x / 100 + x × 100


Here / āχāϝāĻŧāĻžāϤ,


x = 25


25/100 x 100 =20%


Ans / āωāĻ¤ā§āϤ⧰: A) 20%


Q / āĻĒā§ā§°āĻļā§āύ ⧍ :  A number, when 60 is subtracted from 60% of it, gives 60 as the result. Find the number. (āĻāϟāĻž āϏāĻ‚āĻ–ā§āϝāĻžā§° 60% ā§° āĻĒā§°āĻž 60 āĻŦāĻŋāϝāĻŧā§‹āĻ— āϕ⧰āĻŋāϞ⧇, āĻŦāĻŋāϝāĻŧā§‹āĻ—āĻĢāϞ 60 āĻšāϝāĻŧāĨ¤ āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹ āύāĻŋā§°ā§āĻŖāϝāĻŧ āϕ⧰āĻžāĨ¤)


Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš: A) 120 | B) 150 | C) 180 | D) 200


Soln / āϏāĻŽāĻžāϧāĻžāύ


Let the number be x. ((āϧ⧰āĻž āϝāĻžāĻ“āĻ•, āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹ xāĨ¤)


According to the question: āĻĒā§ā§°āĻļā§āύ āĻ…āύ⧁āϏ⧰āĻŋ,



  • 60% of x − 60 = 60

  • 60x / 100 = 60 + 60

  • 60x / 100 = 120

  • 60x = 120 × 100 

  •  x = 120 × 100 / 60

  •  x = 200


Ans / āωāĻ¤ā§āϤ⧰: D) 200


Shortcut:  60% of Number = 60 + 60 = 120 


60% = 120


100% = 120 × 100 / 60


Ans / āωāĻ¤ā§āϤ⧰: D) 200


Q3/āĻĒā§ā§°āĻļā§āύ 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 ? (āϚāĻŋāύāĻŋā§° āĻŽā§‚āĻ˛ā§āϝ 20% āĻŦ⧃āĻĻā§āϧāĻŋ āĻĒā§‹ā§ąāĻžā§° āĻĢāϞāϤ, āϚāĻŋāύāĻŋā§° āĻŦāĻžāĻŦāĻĻ āĻ–ā§°āϚ āĻāϕ⧇ ā§°āĻžāĻ–āĻŋāĻŦāϞ⧈ āĻāϟāĻž āĻĒā§°āĻŋāϝāĻŧāĻžāϞ⧇ āϚāĻŋāύāĻŋā§° āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻ•āĻŋāĻŽāĻžāύ āĻļāϤāĻžāĻ‚āĻļ āĻ•āĻŽāĻžāĻŦ āϞāĻžāĻ—āĻŋāĻŦ ?)


Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš: A) 20% | B) 16⅔% | C) 25% | D) 15%


Soln / āϏāĻŽāĻžāϧāĻžāύ

When the price increases, consumption must decrease to keep expenditure unchanged. (āĻŽā§‚āĻ˛ā§āϝ āĻŦ⧃āĻĻā§āϧāĻŋ āĻĒāĻžāϞ⧇, āĻ–ā§°āϚ āĻāϕ⧇ ā§°āĻžāĻ–āĻŋāĻŦāϞ⧈ āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻ•āĻŽāĻžāĻŦ āϞāĻžāϗ⧇āĨ¤)

Formula / āϏ⧂āĻ¤ā§ā§°: Reduction % = R/(100+R) × 100

where (āχāϝāĻŧāĻžāϤ) R = Percentage Increase in Price ( āĻŽā§‚āĻ˛ā§āϝ āĻŦ⧃āĻĻā§āϧāĻŋā§° āĻļāϤāĻžāĻ‚āĻļ)

= 20/(100 + 20) × 100 = 20/120 × 100 =  16⅔%

Ans / āωāĻ¤ā§āϤ⧰: B) 16⅔%Shortcut:

If the price increases by R%, then the required reduction in consumption is: (āϝāĻĻāĻŋ āĻŽā§‚āĻ˛ā§āϝ R% āĻŦ⧃āĻĻā§āϧāĻŋ āĻĒāĻžāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻ•āĻŽāĻžāĻŦ āϞāĻžāĻ—āĻŋāĻŦ:)

R / (100+R) × 100

For / R = 20%

20/120 × 100 = 6⅔%

Ans / āωāĻ¤ā§āϤ⧰: B) 16⅔%

Q 4 / āĻĒā§ā§°āĻļā§āύ 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? āϝāĻĻāĻŋ āĻāϟāĻž āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§ā§°ā§° āĻĻā§ˆā§°ā§āĻ˜ā§āϝ 20% āĻŦ⧃āĻĻā§āϧāĻŋ āϕ⧰āĻž āĻšāϝāĻŧ āφ⧰⧁ āĻĒā§ā§°āĻ¸ā§āĻĨ 10% āĻšā§ā§°āĻžāϏ āϕ⧰āĻž āĻšāϝāĻŧ, āϤ⧇āĻ¨ā§āϤ⧇ āχāϝāĻŧāĻžā§° āĻ•ā§āώ⧇āĻ¤ā§ā§°āĻĢāϞāϤ āĻ•āĻŋ āĻĒā§°āĻŋāĻŦāĻ°ā§āϤāύ āĻš'āĻŦ?

Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāϏāĻŽā§‚āĻš: A) 10% Increase (āĻŦ⧃āĻĻā§āϧāĻŋ)B) 8% Increase (āĻŦ⧃āĻĻā§āϧāĻŋ)  C) 10% Decrease (āĻšā§ā§°āĻžāϏ)  D) 8% Decrease (āĻšā§ā§°āĻžāϏ)

Soln / āϏāĻŽāĻžāϧāĻžāύ

Using the Successive Percentage Change Formula:

Successive Change = x + y + xy/100

Here / āχāϝāĻŧāĻžāϤ, x = +20, y= −10 x = +20, 

=10 - 2 =

Since the result is positive, the area increases. (āĻĢāϞāĻžāĻĢāϞ āϧāύāĻžāĻ¤ā§āĻŽāĻ• āĻšā§‹ā§ąāĻž āĻŦāĻžāĻŦ⧇ āĻ•ā§āώ⧇āĻ¤ā§ā§°āĻĢāϞ āĻŦ⧃āĻĻā§āϧāĻŋ āĻĒāĻžāϝāĻŧāĨ¤)

Ans / āωāĻ¤ā§āϤ⧰: B) 8% Increase (āĻŦ⧃āĻĻā§āϧāĻŋ)

Shortcut:

For successive percentage changes:

Net Change = x + y + xy/100

Substituting / āĻŽāĻžāύ āĻŦāĻšā§ā§ąāĻžāχ,

20 - 10 + {20×(−10)}/100 

Positive sign ⇒ Increase (āϧāύāĻžāĻ¤ā§āĻŽāĻ• āϚāĻŋāĻšā§āύ ⇒ āĻŦ⧃āĻĻā§āϧāĻŋ)

Ans / āωāĻ¤ā§āϤ⧰: B) 8% Increase (āĻŦ⧃āĻĻā§āϧāĻŋ)