Question

A man bought two cycle for ₹ 1040. He sold one at a loss of 15% and other at a profit of 36% and then he found that each cycle was sold for the same price. Find the C.P. of each cycle.​

Answer 1

Answer:

640 and 400

Step-by-step explanation:

Let the prices are a and b.  

   a + b = 1040  ⇒ a = 1040 - b   ..(1)

        First is sold at 15% loss:

Loss% = (CP - SP)/SP *100%

15%/100% = (a - SP)/a

 0.15 = (a - SP)/a

 SP = a - 0.15a = 0.85a

     2nd is sold at 36% profit:

Profit = (SP - CP)/CP * 100%

36% = (SP - b)/b * 100%

36%/100% = (SP - b)/b

0.36 = (SP - b)/b

 SP = 1.36b

            He sold both at the same price, it means,

SP of 1st = SP of 2nd

0.85a = 1.36b

0.85(1040 - b) = 1.36b     {from (1)}

884 - 0.85b = 1.36b

884 = 1.36b + 0.85b

884 = 2.21b

400 = b      

          hence, a = 1040 - 400

                          = 640

Answer 2

Given :

A man bought two cycles for rs1040. He sold one at loss of 15% and other at a profit of 36% and then he found that each cycle was sold for the same price.

To Find :

Find the C.P. Of each cycle

Solution:

Case 1 :

Let CP of 1 cycle be x

Loss% = 15%

$SP = \frac{CP(100-L\%)}{100}\\SP=\frac{x(100-15)}{100}\\SP=0.85x$

Case 2:

CP of cycle 2 = 1040-x

Profit% = 36%

$SP=\frac{CP(100+P\%)}{100}\\SP=\frac{(1040-x)(100+36)}{100}\\SP=1.36(1040-x)$

Now we are given that  he found that each cycle was sold for the same price.

So, 0.85x=1.36(1040-x)

x=640

Cp of cycle 1 = Rs.640

CP of cycle 2 = 1040-640=400

Hence The CP of cycle 1 is Rs.640 and CP of cylce 2 is Rs.400✅