When a cycle is sold allowing 10% discount on its marked
price a seller gains 5% and allowing 5% discount the profit is
Rs 351. Find the cost price of the cycle. (Ans: Rs. 3240)

The cost price of the cycle is Rs.3240

Represent the cost price of the cycle with x and the selling price with y

A gain of 5% when the marked price is at a discount of 10% implies that:

Express 10% as decimal

Express 5% as decimal

Cross multiply

Collect like terms

This gives

Make y the subject of the formula

Also, when the discount is 5% and the profit is 351, we have:

Express 5% as decimal

This gives

Make y the subject

Substitute

Subtract x from both sides

Take LCM

Multiply both sides by 0.90

Divide both sides by 0.0975

Hence, the cost price of the cycle is Rs.3240

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