Question

Cost price of two bikes is same. One is sold at a profit of 30% and other for Rs.6300 more than the first. If the net profit is 40%. Find the cost price of each bikes.

Answer 1

since , we have given that cost price of two bikes is same.

let the cost price of each bikes be'Rs x'

step1 Find selling price of first bike :
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since , one is sold at 30 % profit ,

so then.

s.p1 = c.p + 30 % of c.p

s.p1 = x + 30 % of x

s.p1 = x + 0.3 x

s.p1 = 1.3 x

profit 1 = s.p1 - c.p

profit 1 = 1.3 x - x = x ( 1.3 - 1 ) = 0.3 x

step 2 Find selling price of 2nd bike:
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given that the selling price of second bike is Rs 6300 more than the selling price of first bike.

s.p2 = s.p1 + Rs 6300

s.p2 = 1.3 x + Rs 6300

profit2= sp2 - c.p

= 1.3 x + 6300 - x

=0.3 x + 6300

Given net profit = 40 %

(profit 1 + profit 2 )/ 2 = 40 % of x

(0.3 x + 0.3 x + 6300 )/ 2 = 40× x /100

0.6 x + 6300 = 2 × 0.4 x

0.6 x + 6300 = 0.8 x

0.8 x - 0.6 x = 6300

0.2 x = 6300

2 x / 10 = 6300

2 x = 63000

x = Rs 31500

therefore ,
cost price of each bikes = Rs 31500

Answer 2

Let the cost price of one bike be x

The cost price of the two bike is 2x

Find the profit on the first bike:

profit = 30% x = 0.3x

Find the profit of the second bike:

Profit = 0.3x + 6300

Profit = 0.3x + 6300

Find total profit for the 2 bikes:

Total profit = 0.3x + 0.3x + 6300

Total profit = 0.6x + 6300

Find the net profit of 40%

Profit = 40% of 2x = 0.4 (2x) = 0.8x

Solve x:

Profit for 2 bikes = 0.6x + 6300

Profit for 2 bikes = 0.8x

0.6x + 6300 = 0.8x

0.2x = 6300

x = 6300 ÷ 0.2

x = Rs 31,500

Answer: The cost price of each bike is Rs 31500