Question

A manufacturer sells his goods to a wholesaler at 10% gain, the wholesaler to the retailer at 20% gain and the retailer to the customer at 30% gain. Find what percent the customer has to pay more on the manufactured price?
(a) 60%
(b) $ 66\dfrac{2}{3}\% $
(c) $ 48\dfrac{1}{5}\% $
(d) $ 71\dfrac{3}{5}\% $

Answer 1

Hint: We will first assume the cost price (CP) of goods let say Rs. 100. Then goods are sold to wholesalers at 10% gain, we will find 10% gain on CP using the formula $ SP=\left( CP+gain\%\cdot CP \right) $. Then this is again sold to retailers at 20% gain. So, here the new cost price (CP) will be the SP of 10%. Similarly, retailer sells these goods to customer so, we will find 30% on new cost price i.e. SP found 20%. Then we will find the difference between original cost price and SP of 30% which we found. On that difference, we have to percentage over cost price and that will be our answer.

Complete step-by-step answer:
Here, we will first assume the price of goods i.e. cost price (CP) to be Rs.100. Now, we are given that the manufacturer sells his goods to wholesalers at 10% gain. So, we will find sells price (SP) on Rs.100 with 10% gain using the formula $ SP=\left( CP+gain\%\cdot CP \right) $
So, using this formula, we will get SP i.e. gain as
 $ SP=\left( 100+10\%\cdot 100 \right) $
On solving, we get
 $ SP=\left( 100+\dfrac{10}{100}\cdot 100 \right) $
 $ SP=Rs.110 $ ………………………………….(1)
Now, the wholesaler sells the goods to retailer at 20% gain. So, the new cost price here will be Rs. 110. So, using the formula $ SP=\left( CP+gain\%\cdot CP \right) $ we will find the sales price SP.
On substituting the values, we will get as
 $ SP=\left( 110+20\%\cdot 110 \right) $
On further simplification, we get as
 $ SP=\left( 110+\dfrac{20}{100}\cdot 110 \right) $
 $ SP=\left( 110+2\cdot 11 \right)=110+22 $
 $ SP=Rs.132 $ ……………………………………..(2)
Now, the retailer sells the goods to customers at 30% gain. So, the new cost price here will be Rs.132. So, using the formula $ SP=\left( CP+gain\%\cdot CP \right) $ we will find sells price SP.
On substituting the values, we will get as
 $ SP=\left( 132+30\%\cdot 132 \right) $
On further simplification, we get as
 $ SP=\left( 132+\dfrac{30}{100}\cdot 132 \right) $
 $ SP=\left( 132+0.3\cdot 132 \right)=132+39.6 $
 $ SP=Rs.171.6 $ ……………………………………..(3)
Now, we know that the original cost price we assumed was Rs.100 and customers have to pay a total of Rs. 171.6. So, finding the difference between both prices we can know that $ =Rs.171.6-Rs.100=Rs.71.6 $ . So, Rs. 71.6 customers have to pay more for goods.
So, finding percentage of 71.6 over Rs.100 we get
 $ =\dfrac{71.6}{100}\times 100 $
 $ =71.6% $
Thus, converting the option from mixed fraction form to fraction we will find option (d) $ 71\dfrac{3}{5}\% $ as an exact match.
Hence, option (d) is the correct answer.

Note: Another approach for solving this problem is by assuming some random variable x and then solving the sum instead of taking Rs.100. We will get the same answer. Also, after finding difference between original price and sell price we do not find a percentage over SP i.e. $ \dfrac{71.6}{171.6}\times 100 $ which will result in a wrong answer. On solving, we will get an answer as 41.72% which is not correct because the percentage should be on original cost price CP, so do not make this mistake.