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Question
A tricycle is sold at a gain of 16%. Had it been sold for Rs 100 more, the gain would have been 20%. Find the C.P. of the tricycle.
Solution
\[\text { Let the S . P of the tricycle be Rs . x and C . P be Rs } . y \]
\[\text { Gain % = 16 % } \]
\[\text { S . P = C . P }\left( \frac{100 + \text { gain % }}{100} \right)\]
\[\text { Then we have, } \]
\[\text { x = y } + \left( \frac{y \times 16}{100} \right)\]
\[\text { x = y + 0 . 16y }\]
\[x = 1 . 16y\]
\[\text { When S . P increases by Rs . 100, we get }\]
\[ \Rightarrow x + 100 = y + \left( \frac{y \times 20}{100} \right)\]
\[\text { Putting x = 1 . 6y, we get }\]
\[ \Rightarrow 1 . 16y + 100 = y + 0 . 2y\]
\[1 . 16y + 100 = 1 . 2y\]
\[0 . 04y = 100\]
\[y = \frac{100}{0 . 04}\]
\[ = 2500\]
\[\text { Thus, C . P of the tricycle is Rs } . 2500 .\]
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