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Sum

A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?

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#### Solution

Let C.P. of the bicycle = Rs.100

**In the I case :**

When Profit = 5% ;

S.P. = Rs. (100+5) = Rs.105

**In the II case :**

C.P. =`(100-30/100xx100)`

= Rs.(100 − 30) = Rs.70

Profit = 30%

S.P. =`((100+"Profit"))/100xx"C.P."`

`=((100+30))/100xx"Rs."70`

`=130/100xx"Rs."70`

= Rs. `(130xx70)/100`

= Rs.91

A difference of two selling prices

= Rs.105 − Rs.91 = Rs.14

If the difference is Rs.14 then C.P. of the bicycle = Rs.100

If the difference is Rs.1 then C.P. of the bicycle = Rs.` 100/14`

If the difference is Rs.63 then C.P. of the bicycle = Rs. `100/14xx63`

= Rs.`(100xx63)/14`

= Rs.50 × 9

= Rs.450

Concept: To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given

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