If successive discounts of 5%, 10% and p% are equivalent to a single discount of 31.6%, then the value of p is: 

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 1)
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  1. 15
  2. 25
  3. 20
  4. 30

Answer (Detailed Solution Below)

Option 3 : 20
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Detailed Solution

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Given:

The successive discounts are 5%, 10% and p%

Single discount = 31.6%

Concept: If there are three successive discounts of a%, b% and c% on MP

SP = MP(100 - a)/100  × (100 - b)/100 × (100 - c)/100 

Formula used:

SP = MP × (100 - D%)/100

D% = (D/MP) × 100

Calculation:

Let MP be x

SP = x × (100 - 5)/100 × (100 - 10)/100 × (100 - p)/100

⇒ SP = x × 95/100 × 90/100 × (100 - p)/100

⇒ x × 95/100 × 90/100 × (100 - p)/100 =  x × (100 - 31.6)/100 

 x × 19/20 × 9/10 × (100 - p)/100 =  x × 68.4/100 

⇒ (100 - p)/100 = 2 × 68.4/171

⇒ (100 - p)/100 = 0.8

⇒ (100 - p) = 80

⇒ p = 20

The value of P is 20%.

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