Question

3. On selling a shirt for 2560, a shopkeeper gains 10%. For how much should he sell it to gain 14%?




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Answer 1

Answer:

2653.09

Step-by-step explanation:

Given,

SP=2560

Gain=100+10=110%

if 110%=2560

  114%=2653.09

Answer 2

➤ Given :-

Selling price of the shirt (1) :- ₹2560

Gain percentage (1) :- 10%

Gain percentage (2) :- 14%

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➤ To Find :-

Selling price if it's sold at 14% of gain.

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➤ Formula required :-

Cost price :-

${\tt \large \dashrightarrow \orange{\boxed{\tt \gray{ \frac{100}{(100 + gain \bf\%)} \times sp}}}}$

Selling price :-

${\tt \large \dashrightarrow \orange{\boxed{\tt \gray{ \frac{(100 + gain \bf\%)}{100} \times cp}}}}$

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★ How to do :-

Here, we are given that a shirt was sold for 2560 rupees by obtaining 10% of gain. Next, the same shirt is sood for 14% of gain. We should find the selling price of the second statement. So, first we should find the cost price of the first statement i.e, the shirt is sold at 2560. We can use the first formula for finding that. Next, by using the cost price obtained here for finding the selling price of the second statement. For finding that, we should use the second formula given. So, let's solve!!

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➤ Solution :-

Cost price of first statement :-

${\tt \leadsto \dfrac{100}{(100 + 10)} \times 2560}$

${\tt \leadsto \dfrac{100}{\cancel{110}} \times \cancel{2560} = \dfrac{100}{11} \times 256}$

${\tt \leadsto \dfrac{100 \times 256}{11} = \dfrac{25600}{11}}$

${\tt \leadsto \cancel \dfrac{25600}{11} = \boxed{\tt 2327.27}}$

Now,

Selling price of second statement :-

${\tt \leadsto \dfrac{(100 + 14)}{100} \times 2327.27}$

${\tt \leadsto \dfrac{114}{100} \times 2327.27}$

${\tt \leadsto \dfrac{114 \times 2327.27}{100} = \dfrac{265308.78}{100}}$

${\tt \leadsto \cancel \dfrac{265308.78}{100} = \boxed{\tt rs \: \: 2653.08}}$

$\Huge\therefore$ The selling price of the shirt by gaining 14% of gain is ₹2653.08.

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$\dashrightarrow$ Some related formulas :-

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