Question

A man bought 2 TV sets for RS 42500. He sold one at loss of 10% and other at a profit of 10% If SellingPrice of each TV is same. Find cost Price of each set.

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Answer 1

Step-by-step explanation:

Given that he bought 2 TV sets for 42500.

Let the cost price one TV set be x.

∴ Cost price of other set = 42500 - x.

(1)

He sold one at loss of 10%.

Selling price of first TV = 90% of x

= (90/100) * x

= 9x/10

(2)

Other at a profit of 10%

Selling price of other tv set = 110% of (42500 - x)

= 11/10 (42500 - x)

Now,

9x/10 = (11/10) * (42500 - x)

⇒ 9x = 11(42500 - x)

⇒ 9x = 11 * 42500 - 11x

⇒ x = 23375

Then,

Cost price of other TV set = 42500 - 23375

                   

                                           = 19125.

Therefore,

Cost price of first TV set = 23375

Cost price of another TV set = 19125

Hope it helps!

Answer 2

Solution :

Let the Cost Price of first TV set be Rs x. Then,

Cost Price of second TV = Rs(42500-x)

Loss on 1st TV set = 10%

$\implies \sf \: \cancel \dfrac{10}{100} \times x$

$\implies \sf \:Rs \: \dfrac{x}{10}$

Selling Price of 1st TV set =

$\implies \sf \: Rs(x - \dfrac{x}{10} ) = Rs \: \dfrac{9x}{10}$

Gain on second TV set =

$\hookrightarrow \sf \: 10\% \: of \: Rs(42500 - x)$

$\hookrightarrow \sf \: Rs \: \dfrac{10}{100} \times (42500 - x)$

$\hookrightarrow \sf \: Rs \: (\dfrac{42500 - x}{10} )$

$\therefore \sf \: S.P \: of \: second \: TV \: set = \\ \sf \: \: \: \: \: C.P + Gain$

$\hookrightarrow \sf \: Rs(42500 - x) + Rs (\dfrac{42500 - x}{10} )$

$\hookrightarrow \sf \: Rs(42500 - x) + (1 + \dfrac{1}{10} )$

$\hookrightarrow \sf \: Rs(42500 - x) + \dfrac{11}{10}$

It is given that S.P of each set is same

$\therefore \sf \: \dfrac{9x}{10} = (42500 - x) \times \dfrac{11}{10}$

$\hookrightarrow \sf \: 9x = (42500 - x) \times 11$

$\hookrightarrow \sf \: 9x = 42500 \times 11 - 11x$

$\hookrightarrow \sf \: 11x + 9x = 42500 \times 11$

$\hookrightarrow \sf \: 20x = 42500 \times 11$

$\hookrightarrow \sf \: x = \cancel\dfrac{42500 \times 11}{20}$

$\hookrightarrow \sf \: x = \large \boxed{ \sf \: Rs \: 23375}$

Hence, C.P of first TV set = Rs 23375

C.P of another TV set =

$\sf \: Rs \: (42500 - 23375)$

$\large \boxed{ \sf \: Rs \: 19125}$