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.

Answer 1

\[\text { Let the S . P of the tricycle be Rs . x and C . P be Rs } . y \]

\[\text { Gain % = 16 % } \]

\[\text { S . P = C . P }\left( \frac{100 + \text { gain % }}{100} \right)\]

\[\text { Then we have, } \]

\[\text { x = y } + \left( \frac{y \times 16}{100} \right)\]

\[\text { x = y + 0 . 16y }\]

\[x = 1 . 16y\]

\[\text { When S . P increases by Rs . 100, we get }\]

\[ \Rightarrow x + 100 = y + \left( \frac{y \times 20}{100} \right)\]

\[\text { Putting x = 1 . 6y, we get }\]

\[ \Rightarrow 1 . 16y + 100 = y + 0 . 2y\]

\[1 . 16y + 100 = 1 . 2y\]

\[0 . 04y = 100\]

\[y = \frac{100}{0 . 04}\]

\[ = 2500\]

\[\text { Thus, C . P of the tricycle is Rs } . 2500 .\]