Page 187 - Start Up Mathematics_8 (Non CCE)

Ê 100 + Profit% ˆ Ê 100 12+ ˆ Ê 112 ˆ
S.P. = Á Ë 100 ˜ × C.P. = ` Á Ë 100 ¯ × 980 = ` Á Ë 100 ¥ 980 = ` 1,097.60
˜
˜
¯
¯
\ S.P. of a cricket bat = ` 1,097.60
Discount % = 20%
Ê 100 ¥S.P. ˆ Ê 100 1 097 60¥ , . ˆ Ê 109 760, , ˆ
\ M.P. = Á 100 - Discount% ˜ ¯ = ` Á 100 20- ˜ ¯ = ` Á 80 ˜ ¯ = ` 1,372
Ë
Ë
Ë
Hence, the sports dealer must mark each cricket bat at ` 1,372.
Example 19: A trader buys certain items at 30% off the list price and he wishes to make a profit of 20%
after allowing a discount of 20%. At what percent above the list price should he mark the
items?
Solution: Let the list price of the item be ` 100.
Suppose the trader marks the price x% above the list price, then
M.P. = ` (100 + x)
Discount % on list price = 30%

fi Discount on list price = ` 30
\ C.P. of the item = ` (100 – 30) = ` 70
Profit % = 20%

Ê 100 + Profit% ˆ Ê 100 20+ ˆ
\ S.P. = Á Ë 100 ˜ × C.P. = ` Á Ë 100 ˜ ¯ ¥ 70
¯

Ê 120 ˆ
S.P. = ` Á Ë 100 ¥ 70 = ` 84 ...(1)
˜
¯
M.P. = ` (100 + x), Discount % = 20%

Ê 100 - Discount% ˆ Ê 100 20- ˆ
\ S.P. = Á Ë 100 ˜ ¯ × M.P. = ` Á Ë 100 ˜ ¥ ( 100 + )x
¯

80
8
= ` Ê 100 ¥ ( 100 + )x ˆ ˜ ¯ = ` 10 ( 100 + x )
Á
Ë
4
S.P. = ` ( 100 + x ) ...(2)
5
From (1) and (2), we have

4
(100 + x) = 84
5
84 5¥
fi 100 + x = = 105
4
fi x = 105 – 100 = 5
Hence, the trader should mark the items 5% above the list price.
Example 20: Find a single discount equivalent to two successive discounts of 25% and 15%.
Solution: Let the M.P. of an article be ` 100.

First discount = ` 25
\ S.P. after first discount = ` (100 – 25) = ` 75

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