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प्रश्न
A manufacturer makes clear profit of 30% on cost after allowing 35% discount. If the cost of production rises by 20%, by what percentage should he reduce the rate of discount so as to make the same rate of profit keeping his list prices unaltered.
उत्तर
Let the list price be ₹ 100.
Since, the manufacturer allows 35% discount on list price.
Discount = 35% of list price
= 35% of ₹ 100
`= 35/100 xx 100` = ₹ 35
Now, selling price = List price – Discount
= 100 - 35 = ₹ 65
Also, he gets 30% profit on cost price.
Let the cost price be ₹ x
∵ Selling price = Cost price + Profit
∴ 65 = x + 30% of ₹ x
∴ `65 = x + 30/100 xx x`
∴ `65 = (100 x + 30x)/100`
∴ `65 = (130 x)/100`
∴ `(65 xx 100)/130` = x
∴ x = ₹ 50
∴ Cost price is ₹ 50.
Given, the cost of production rises by 20%
∴ New cost price = Old cost price + Rise in cost price
= 50 + 20% of old cost price
= 50 + 20% of ₹ 50
`= 50 + 20/100 xx 50 = 50 + 10`
∴ New cost price = ₹ 60
The rate of profit is to remain same.
New selling price = new cost price + profit
= 60 + 30% of new cost price
`= 60 + 30/100 xx 60`
= 60 + 18
∴ New selling price = ₹ 78
But, here the list price remains the same.
∴ New selling price = List price – New discount
∴ 78 = 100 – New discount
∴ New discount = 100 – 78
∴ New discount = ₹ 22
∴ Rate of new discount = `"New Discount"/100 xx "List Price"`
`= 22/100 xx 100` = 22%
∴ Reduction in discount (%)
= Old discount (%) – New discount (%)
= 35% - 22%
= 13%
∴ Rate of discount should be reduced by 13 % to make the same rate of profit.
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