Answer
Verified
393.9k+ views
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.
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.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE