Question

a cycle was sold at a gain of 10% add it is been sold for rs 70 more then again have been 15% find cost price of the cycle​

Answer 1

GIVEN:

★A cycle is sold at the gain of 10%.

★Had it been sold for Rs 70 more, then the gain would have been 15%.

TO FIND:

★The cost price of the cycle.

ANSWER:

Let us take the CP if the cycle be x.

First case:

Gain = 10%.

We know that, SP =

$\large\green{\boxed{SP =CP×\dfrac{100+gain\:percent}{100}}}$

=>$SP =x×\dfrac{100+10}{100}$

=>$SP = \dfrac{110x}{100}$

.°. $SP = \dfrac{11x}{10}$

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By question

If it is sold at Rs 70 more then gain would be 15%.

So, SP at a gain of 15%=

$\large{\purple{\dfrac{11x}{10}+70}}$ ........... (1)

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Second case,

Gain=15%

CP = x (supposed)

So, again,

$\large\blue{\boxed{SP =CP×\dfrac{100+gain\:percent}{100}}}$

=> $SP = x ×\dfrac{100+15}{100}$

=>$SP =\dfrac{115x}{100}$

.°. $SP =\dfrac{23x}{20}$

But earlier it was found, $\dfrac{11x}{10}+70}$

So, Atq,

=>$\dfrac{11x}{10}+70}=\dfrac{23x}{20}$

=>$\dfrac{11x+700}{10}=\dfrac{23x}{20}$

=>$2(11x+700)=23x$

=>$22x+1400=23x$

=>$23x-22x=1400$

.°. $x = Rs 1400$

Therefore the CP of the cycle is Rs 1400.

$\huge\orange{\boxed{Cost\:Price=Rs1400}}$