1.

A single discount equivalent to a discount series of 5%, 10%, 15% and 20% is:1. 43.86%2. 42.86%3. 40.86%4. 41.86%

Answer» Correct Answer - Option 4 : 41.86%

Given:

A series of Discounts 5%, 10%, 15%, 20%

Formula Used: 

 Equivalent = A + B + (AB)/100

Calculation:

Discount is written as negative 

 Equivalent discount for 5% and 10% = (– 5) + (–10) + {(– 5) × (– 10)}/100

⇒ (– 5) + (– 10) + (0.5)

⇒ (– 15 + 0.5)

⇒ (– 14.5)

⇒ Equivalent Discount for 5% and 10% = 14.5%

Now, Equivalent discount for 14.5% and 15% = (– 14.5) + (– 15) + {(– 14.5) × (– 15)}/100

⇒ (– 14.5) + (– 15) + (2.175)

⇒ (– 29.5 + 2.175)

⇒ (– 27.325)

⇒ Equivalent Discount for 5%, 10% and 15% = 27.325%

Now, Equivalent discount for 27.325% and 20% = (– 27.325) + (– 20) + {(– 27.325) × (– 20)}/100

⇒ (– 27.325) + (– 20) + (5.465)

⇒ (– 47.325 + 5.465)

⇒ (– 41.86)

⇒ Equivalent Discount for 5%, 10%, 15% and 20% = 41.86%

∴  A single discount equivalent to a discount series of 5%, 10%, 15% and 20% is 41.86%.


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