Question

A cycle was sold at a gain of 10%. Had it been sold for 260RS. more, the gain would have been 14%. Find the cost price of the cycle.​

Answer 1

Answer:

Cost price of the cycle is Rs 6500.

Step-by-step explanation:

Let the original cost price be 'x'. It is sold at a gain of 10%, so

selling price = x(1 + r/100)

                    = x(1 + 10/100)

                    = (11x/10)

If it had been sold for 260Rs more, the gain would have been 14%:

CP = x   ;  SP = (11x/10) + 260 ; gain = 14%

        Using, gain% = (SP - CP)/CP * 100%

⇒ 14% = ((11x/10)+260 - x)/x  * 100%

⇒ 14x = (x/10 + 260) * 100

⇒ 14x = 10x + 26000

⇒ 14x - 10x = 26000

⇒ 4x =26000

⇒ x = 6500

Answer 2

Given :-

A cycle was sold at a gain of 10%. Had it been sold for 260RS. more, the gain would have been 14%

To Find :-

CP

Solution :-

Let the SP be x

Gain = 10%

Gain = x + 10% of x

Gain = x + 10/100x

Gain = 100x + 10x/100

Gain = 110x/100

Now,

Gain = 14%

Gain = x + 14% of x

Gain = x + 14/100x

Gain = 100x + 14x/100

Gain = 114x/100

114x/100 = 110x/100 + 260

114x/100 - 110x/100 = 260

4x/100 = 260

x/25 = 260

x = 25 × 260

x = 6500