Percentage
- A reduction of 20% in the price of an apple enables a man to buy 10 apples more for ₹ 54. The reduced price of apples per dozen is
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Let the original price of apples be ₹ x/ dozen
∴ New price = ₹ 4x = /dozen 5 ∴ 54 - 54 = 10 4x x 12 5 ⇒ 54 
5 - 1 
= 5 4x x 6 ⇒ 54 5 - 4 = 5 4x 6 ⇒ 54 - 5 ⇒ 4x = 54 × 6 4x 6 5 ∴ 4x = 54 × 6 = ₹ 12.96 5 5 × 5
Aliter : Using Rule 31,Reduced price = 20 × 54 100 × 10 12 = 1080 × 12 = ₹ 12.96 per kg 1000 Correct Option: B
Let the original price of apples be ₹ x/ dozen
∴ New price = ₹ 4x = /dozen 5 ∴ 54 - 54 = 10 4x x 12 5 ⇒ 54 5 - 1 = 5 4x x 6 ⇒ 54 5 - 4 = 5 4x 6 ⇒ 54 - 5 ⇒ 4x = 54 × 6 4x 6 5 ∴ 4x = 54 × 6 = ₹ 12.96 5 5 × 5
Aliter : Using Rule 31,Reduced price = 20 × 54 100 × 10 12 = 1080 × 12 = ₹ 12.96 per kg 1000
- Due to an increase of 50% in the price of eggs, 4 eggs less are available for ₹ 24. The present rate of eggs per dozen is :
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The original price of 1 egg = ₹ x
Present price = ₹ 3 x 2 ∴ 24 - 24 = 4 x 3x 2 ⇒ 24 1 - 2 = 4 x 3 ⇒ 8 = 4 ⇒ x = 2 x
∴ Present price of eggs per dozen= 12 × 3 × 2 = ₹ 36 x
Aliter : Using Rule 31,New price = 50 × 24 = ₹ 36 100 × 4 12 Correct Option: C
The original price of 1 egg = ₹ x
Present price = ₹ 3 x 2 ∴ 24 - 24 = 4 x 3x 2 ⇒ 24 1 - 2 = 4 x 3 ⇒ 8 = 4 ⇒ x = 2 x
∴ Present price of eggs per dozen= 12 × 3 × 2 = ₹ 36 x
Aliter : Using Rule 31,New price = 50 × 24 = ₹ 36 100 × 4 12
- A reduction of 20% in the price of wheat enables Lalita to buy 5 kg more wheat for j 320. The original rate (in rupees per kg) of wheat was
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Original price of wheat = ₹ x /kg.
New price of wheat= ₹ 4x / kg 5 ∴ 320 - 320 = 5 4x x 5 ⇒ 320 5 – 1 = 5 4x x ⇒ 320 5 – 4 = 5 4x ⇒ 320 = 5 4x ⇒ x = 320 = ₹ 16 4 × 5
Aliter : Using Rule 31,New price = 20 × 320 100 × 5 = 1280 = ₹ 12.8 100
Let the original price be ₹ x per kg⇒ x - 20x = 12.8 100
80x = 12.8 × 100x = 1280 = 16 per kg 80 Correct Option: A
Original price of wheat = ₹ x /kg.
New price of wheat= ₹ 4x / kg 5 ∴ 320 - 320 = 5 4x x 5 ⇒ 320 5 – 1 = 5 4x x ⇒ 320 5 – 4 = 5 4x ⇒ 320 = 5 4x ⇒ x = 320 = ₹ 16 4 × 5
Aliter : Using Rule 31,New price = 20 × 320 100 × 5 = 1280 = ₹ 12.8 100
Let the original price be ₹ x per kg⇒ x - 20x = 12.8 100
80x = 12.8 × 100x = 1280 = 16 per kg 80
- Due to an increase of 20% in the price of eggs, 2 eggs less are available for ₹ 24. The present rate of eggs per dozen is :
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Original rate = ₹ x per egg
New rate = ₹ 6x per kg 5 ∴ 24 - 24 × 5 = 2 x 6x ⇒ 24 - 20 = 2 x x ⇒ 4 = 2 ⇒ x = 2 x ∴ New rate = 4 = 2 ⇒ x = 2 x
∴ Rate per dozen of eggs= ₹ 12 × 12 = ₹ 28.80 5
Aliter : Using Rule 31,
New price/present price= 20 × 24 = ₹ 28.80 100 × 2 12 Correct Option: D
Original rate = ₹ x per egg
New rate = ₹ 6x per kg 5 ∴ 24 - 24 × 5 = 2 x 6x ⇒ 24 - 20 = 2 x x ⇒ 4 = 2 ⇒ x = 2 x ∴ New rate = 4 = 2 ⇒ x = 2 x
∴ Rate per dozen of eggs= ₹ 12 × 12 = ₹ 28.80 5
Aliter : Using Rule 31,
New price/present price= 20 × 24 = ₹ 28.80 100 × 2 12
- A reduction of 25% in the price of rice enables a person to buy 10 kg more rice for ₹ 600. The reduced per kg price of rice is
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Let original price of rice per kg = ₹ x (let)
∴ New price of rice per kg= ₹ 3x 4 ∴ 600 - 600 = 10 3x x 4 ⇒ 600 4 – 1 = 10 3x x ⇒ 600 4 – 3 = 10 3x ⇒ 600 = 10 3x ⇒ x = 600 = ₹ 20 30 ∴ New price = 3x - 3 × 20 = ₹ 15/kg 4 4
Method 2 :
Quicker Approach
If the price of an article is reduced by a% and buyer gets c kg more for some ₹ b, the newprice per kg of article = ab 100 × c = 25 × 600 = ₹ 15 100 × 10
Aliter : Using Rule 31,
Reduced price per kg= 25 × 600 = ₹ 15 100 × 10 Correct Option: D
Let original price of rice per kg = ₹ x (let)
∴ New price of rice per kg= ₹ 3x 4 ∴ 600 - 600 = 10 3x x 4 ⇒ 600 4 – 1 = 10 3x x ⇒ 600 4 – 3 = 10 3x ⇒ 600 = 10 3x ⇒ x = 600 = ₹ 20 30 ∴ New price = 3x - 3 × 20 = ₹ 15/kg 4 4
Method 2 :
Quicker Approach
If the price of an article is reduced by a% and buyer gets c kg more for some ₹ b, the newprice per kg of article = ab 100 × c = 25 × 600 = ₹ 15 100 × 10
Aliter : Using Rule 31,
Reduced price per kg= 25 × 600 = ₹ 15 100 × 10
