Question

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.

Answer 1

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.