Question

b) Find a single discount equivalent to two successive discounts of 20%and
15%​

Answer 1

Answer:

25%

Step-by-step explanation:

Answer 2

Question -

Find a single discount equivalent to two successive discounts of 15% and 20%.

Given -

• Two successive discounts - 15% and 20%

To Find -

• A single discount equivalent to the two successive discounts.

Solutions -

$\sf\underline{{✇Method \: 1 \: }{: }}$

Let a single discount of d% be equivalent to the two successive discounts.

Then, (SP after a discount of d%) = (SP after the two successive discounts of 15% and 20%).

$\sf{{:⟼ \: (1 - \frac{d}{100}) \: \times \: MP}{ \: = \:(1 - \frac{15}{100})(1 - \frac{20}{100}) \times MP }}$

$\sf{{:⟼ \:1 - \frac{d}{100} = \: \frac{17}{20}. \frac{4}{5} = }{ \: \frac{17}{25} }}$

$\sf{{ :⟼ \: \frac{d}{100} \: = \:1 - \frac{17}{25} }{\: = \frac{8}{25} }}$

$\sf{{ :⟼\:d = \: \frac{8}{25} \times 100 }{ = \: 32.}}$

Hence, the single equivalent discount is 32%.

_______________________________________

$\sf\underline{{✇ \:Method \:2 }{ \:(Alternative \: method) \:: }}$

Here,

• d¹ = 15
• d² = 20

$\sf{{⟹ \: (SP\: after\:two \: discounts \: of \: 15\% \: and \: 20\% ) = (1 - \frac{d¹}{100})(1 - \frac{d²}{100} ) \times MP }{ \: }}$

$\sf{{:⟼\: (1 - \frac{15}{100})(1 - \frac{20}{100}) \: }{ \times \: MP }}$

$\sf{{ :⟼\: \frac{17}{20} \times \frac{4}{5} \times \: MP \: }{ = \frac{17}{25} \: \times MP }}$

$\sf{{:⟼\: \frac{68}{100} \times \:MP }{ \: = (1 - \frac{32}{100}) \times MP }}$

$\sf{{☞ \: (SP\:after \: a}{ \: single \: discount \: of \: 32\%).}}$

Hence, The single discount equivalent to the two successive discounts is 32%.

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Remember These -

:⟼ Discount = MP - SP.

:⟼ SP = MP - discount.

:⟼ MP = SP + discount.

:⟼ Discount per cent = discount/MP × 100

:⟼ After a discount of d% on the MP,

SP = (1 - d/100) × MP

:⟼ After two successive discounts of d¹% and d²% on the MP,

SP = (1 - d¹/100)(1 - d²/100) × MP

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