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Mathematics

Assertion (A) : Two successive discounts of 10% and 5% are equal to a single discount of 1412%14\dfrac{1}{2}\%.

Reason (R) : Rate of discount = DiscountS.P.×100%\dfrac{\text{Discount}}{\text{S.P.}} \times 100\%.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Profit, Loss & Discount

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Answer

Let M.P. = ₹ 100

1st discount = 10% of ₹ 100

= ₹ 10100×100\dfrac{10}{100} \times 100

= ₹ 10

Discounted price = ₹ 100 - ₹ 10 = ₹ 90

2nd discount = 5% of ₹90

= ₹ 5100×90\dfrac{5}{100} \times 90

= ₹ 4.50

Final discounted price = ₹ 90 - ₹ 4.5 = ₹ 85.50

Total discount = M.P. - Final discounted price

= ₹ 100 - ₹ 85.5 = ₹ 14.5

Since the discount of ₹ 14.5 is on ₹ 100.

∴ Single equivalent discount%

=Total discount100×100%=14.5100×100%=14.5%= \dfrac{\text{Total discount}}{100} \times 100\% \\[1em] = \dfrac{14.5}{100} \times 100\% \\[1em] = 14.5\%

So, assertion (A) is true.

By formula,

Discount % = DiscountM.P.×100%\dfrac{\text{Discount}}{\text{M.P.}} \times 100\%

So, reason (R) is false.

Hence, option 3 is the correct option.

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