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Theta having a gain of Rs. 1500 when he sells the Geyser at a 10% gain and an Oven at 5% loss. But, if he sells the Geyser at 5% gain and an Oven at 10% gain, he gains Rs. 4500. Find the actual cost of the Geyser and that of an Oven.

Theta having a gain of Rs. 1500 when he sells the Geyser at a 10% gain and an Oven at 5% loss. But, if he sells the Geyser at 5% gain and an Oven at 10% gain, he gains Rs. 4500. Find the actual cost of the Geyser and that of an Oven. Correct Answer Rs. 50,000; Rs. 20,000

Given:

Theta having a gain of Rs. 1500 when he sells the Geyser at a 10% gain and an Oven at 5% loss. But, if he sells the Geyser at 5% gain and an Oven at 10% gain, he gains Rs. 4500.

Formula Used:

Profit% = (S.P. – C.P.)/C.P × 100

Loss% = (C.P. – S.P.)/C.P × 100

Calculation:

Let the cost price of the Geyser be Rs x and that of an Oven be Rs. y.

Then, total C.P. of Geyser and of an Oven = Rs. (x + y).

S.P. in first case = Rs. (110x/100 + 95y/100) = Rs. (11x/10 + 19y/20)

Gain in this case = Rs. (11x/10 + 19y/20) – (x + y) = Rs. (x/10 – y/20)

So, x/10 – y/20 = 1,500

⇒ 2x – y = 30,000       ----(1)

S.P. in second case = Rs. (105x/100 + 110y/100) = Rs. (21x/20 + 11y/10)

So gain in this case = Rs. (21x/20 + 11y/10) – (x + y) = Rs. (x/20 + y/10)

So, x/20 + y/10 = 4,500

Or, x + 2y = 90,000      ----(2)

Multiply eq. (1) by 2 and the add the result with eq. (2), we get

3x = 60,000 + 90,000 = 1,50,000

⇒ x = 1,50,000/3

⇒ x = 50,000

Putting x = 50,000 in eq. (2), we get

50,000 + 2y = 90,000

⇒ 2y = 90,000 – 50,000 = 40,000

⇒ y = 40,000/2

⇒ y = 20,000

∴ the cost of the Geyser is Rs. 50,000 and that of an Oven is Rs. 20,000.

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