Page 116 - ICSE Math 8

Example 11: 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 per cent 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% ⇒ Discount on list price = ` 30

∴ C.P. of the item = ` (100 – 30) = ` 70
Profit % = 20%
+
Ê 100 + Profit% ˆ Ê 100 20ˆ
∴ 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 20ˆ
∴ S.P. = Á Ë 100 ˜ ¯ × M.P. = ` Á Ë 100 ˜ ¥ ( 100 + )x
¯
Ê 80 ˆ 8 4
= ` Á 100 ¥ ( 100 + )x ˜ ¯ = ` 10 ( 100 + x or, S.P. = ` ( 100 + x ) ...(2)
)
Ë
5
From (1) and (2), we have
4 84 5×
(100 + x) = 84 ⇒ 100 + x = = 105 ⇒ x = 105 – 100 = 5
5 4
Hence, the trader should mark the items 5% above the list price.

Successive discounts
When two or more discounts are allowed on a product one after the other, then such discounts are known as
successive discounts. For example, if a discount of 20% is given on an article and then another discount of
15% is given on its reduced price, then 20% and 15% are said to be successive discounts.
Single discount, D% equivalent to two successive discounts of D % and D % is given by:
1
2
D × D
D% = D + D – 1 100 2 %
1
2
Selling price after successive discounts of D , D , ..., D on the marked price (M.P.) is given by:
2
n
1
D D D
S.P. = 1 – 1 1 – 2 … 1 – n × M.P.
100 100 100
Example 12: Find a single discount equivalent to two successive discounts of 25% and 15%.
Solution: Let M.P. be ` 100.
D % = 25%, D % = 15%
1
2
Ê 100 - D % ˆ Ê 100 - D % ˆ Ê 100 25- ˆ Ê 100 15ˆ
-
S.P. = Á Ë 100 1 ˜ Á 100 2 ˜ × M.P. = ` Á 100 ˜ Á 100 ¯ ˜ × 100
¯ Ë
¯
Ë
¯ Ë
Ê 75 85 ˆ
= ` Á ¥ ¥ 100 = ` 63.75
˜
¯
Ë
Discount = ` (100 – 63.75) = ` 36.25 100 100
Ê 36 25. ˆ
∴ Discount % = Á Ë 100 ¥ 100 % = 36.25%
˜
¯
1
Hence, single equivalent discount = 36.25% = 36 %
4
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