Question

Ram sold to Shyam an article with 20% profit. Shyam sold
same article for Rs. 504 with 5% profit to Ghanashyam.
How much did it cast for Ram?
(Ans: Rs. 400​

Answer 1

➤ Correct Question :-

Ram sold to Shyam an article with 20% profit. Shyam sold same article for Rs. 504 with 5% profit to Ghanashyam. Find the cost price and the selling price of Ram.

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➤ Given :-

Profit percent of Ram :- 20%

Selling price of Shyam :- ₹504

Profit percent of Shyam :- 5%

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➤ To Find :-

The cost price and the selling price of Ram.

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★ How to do :-

Here, we are given with the profit percentage obtained yo Ram and the selling price of Shyam and also the profit percentage obtained to Shyam. We are asked to find the cost price and the selling price of Ram. So, first we should find the cost price of Shyam. This cost price of Shyam is equal to selling price of Ram. By using the selling price and the profit percent of Ram, we can easily find the cost price. So, let's solve!!

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➤ Solution :-

Selling price of Ram :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{100}{(100 + Profit \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 + 5)} \times 504}$

First, add the values in denominator of the fraction and write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{100}{105} \times 504 = \dfrac{20}{21} \times 504}$

Now, multiply both the numbers.

${\tt \leadsto \dfrac{20 \times 504}{21} = \dfrac{10080}{21}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{10080}{21} = \pink{\underline{\boxed{\tt Rs \: \: 480}}}}$

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Now, let's find the cost price of Ram.

Cost price of Ram :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{100}{(100 + Profit \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 + 20)} \times 480}$

First, add the values in denominator of the fraction and write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{100}{120} \times 480 = \dfrac{5}{6} \times 480}$

Write the denominator and the whole number in lowest form by cancellation method.

${\tt \leadsto \dfrac{5}{\cancel{6}} \times \cancel{480} = \dfrac{5}{1} \times 80}$

Now, add the remaining numbers.

${\tt \leadsto \dfrac{5 \times 80}{1} = \pink{\underline{\boxed{\tt Rs \: \: 400}}}}$

$\Huge\therefore$ The selling of Ram is ₹480 and the cost price of Ram is ₹400.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\\bigstar \: \sf{S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array}}$