Page 188 - Start Up Mathematics_8 (Non CCE)

Ê 15 ˆ
Second discount = 15% of ` 75 = ` Á Ë 100 ¥ 75 = ` 11.25
˜
¯
\ S.P. after second discount = ` (75 – 11.25) = ` 63.75

\ Net S.P. = ` 63.75
Single discount equivalent to given successive discounts = (100 – 63.75)%
1
= 36.25% or 36 %
Alternate Method 4
Let M.P. be ` 100
D % = 25%, D % = 15%
2
1
Ê 100 - D % ˆ Ê 100 - D % ˆ Ê 100 25- ˆ Ê 100 15- ˆ
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 %
Example 21: The marked price of a blanket is ` 1,000. After two successive discounts it is sold for ` 630.
If the first discount is 30%, what is the rate of the second discount?
Solution: M.P. of a blanket = ` 1,000
First discount (D %) = 30%
1
S.P. of blanket = ` 630
Let the second discount be D %.
2
Ê 100 - D % ˆ Ê 100 - D % ˆ
S.P. = Á Ë 100 1 ˜ Á 100 2 ˜ × M.P.
¯
¯ Ë
70 ˆ Ê
fi 630 = Ê Á Ë 100 30- ˆ Ê 100 - D% ˆ ˜ ¯ × 1,000 = Ê Á Ë 100¯ Ë 100 - D% ˆ ˜ ¯ ¥ ,
2
2
1 000
˜ Á
˜ Á
¯ Ë
100
100
100
630 100 100¥ ¥
fi 100 – D % =
2
70 1 000¥ ,
fi 100 – D % = 90
2
fi D % = 100 – 90 = 10%
2
Hence, the rate of the second discount is 10%.
Alternate Method
M.P. of the blanket = ` 1,000
Ê 30 ˆ
First discount = 30% of ` 1,000 = ` Á 100 ¥ 1 000, ˜ = ` 300
¯
Ë
S.P. of the blanket after the first discount = ` (1,000 – 300) = ` 700
Ê D ˆ
2
Second discount = D % of ` 700 = ` Á 100 ¥ 700 = ` (7D )
˜
2
2
¯
Ë
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