Question

A cycle was sold at a gain of 19%.Had it been sold for ₹ 260 more, the gain would have been 14%. Find the cost of the cycle.​

Answer 1

$\sf{\underline{\underline{ \purple{ \large{Answer:}}}}}$

❀ Rs. 5200

$\\ \sf{\underline{\underline{ \purple{ \large{Step-by-step \: Explanation:}}}}}$

Let the C.P of cycle be x

$\underline{ \boxed{ \sf{S.P. = \frac{(100 + gain\%)}{100} \times C.P.}}}$

When the cycle is sold at 19% profit, then S.P is,

$\\ \implies {\sf{S.P. = \frac{(100 + 19)}{100} \times x }}$

$\implies {\sf{S.P. = \frac{119}{100} \times x }}$

$\implies {\sf{S.P. = \frac{119}{100} x }}$

When the cycle is sold at 14% profit, then S.P is,

$\\ \implies {\sf{S.P. = \frac{(100 + 14)}{100} \times x }}$

$\implies {\sf{S.P. = \frac{114}{100} \times x }}$

$\implies {\sf{S.P. = \frac{114}{100} x }}$

Now, we know that it had been sold for ₹ 260 more,

$\\ \sf{\implies{\frac{119}{100} x - \frac{114}{100} x = 260}}$

$\sf{\implies{ \frac{119x - 114x}{100} = 260}}$

$\sf{\implies{ \frac{5x}{100} = 260}}$

$\sf{\implies{ 5x = 260 \times 100}}$

$\sf{\implies{ 5x = 26000}}$

$\sf{\implies{ x = \frac{26000}{5}}}$

$\sf{\implies{ x = \frac{ \cancel{26000}}{ \cancel5}}}$

$\sf{\implies{ x = 5200}}$

∴ The cost price i.e ,C.P = $\green{ \underline{ \boxed{ \sf{Rs. \: 5200}}}}$

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