Question

A person sells Tv at 25%profit.If he gets profit equal to 25%sp then he would gain (5%cp+rs.80)more.Find the cp of Tv?

Answer 1

Let CP of TV be x
So, he sells as 25% profit
SP or Price at which he sells = 125% of CP = 1.25x
And his profit = 0.25x

Now, if he gets profit = 25% SP = 25% of (1.25x)

= 1/4 1.25x = 0.3125x
This profit = Earlier Profit + 5% CP + 80

0.3125x = 0.25x + (0.05x + 80)
0.3125x = 0.3x + 80

0.0125x = 80
x = 6400
Therefore, Cost Price = Rs. 6400

Answer 2

Given conditions ⇒

Profit % = 25 %.
Price at which the T.V. sells = 25% of the Cost Price.
Profit = 25/100 × C.P.
Profit = C.P./4
∴ C.P. = 4 × Profit.

Now, S.P. of the T.V. = C.P. + Profit
= C.P. +  C.P./4
= 5/4 of C.P.

A/c to the Question,
 New Profit = 25 % of the S.P.
 = 25% of 5/4 of C.P.
 = 1/4 × 5/4 × C.P.
 = 5/16 C.P.
 = 5 C.P./16

A/c to the given statement,
New Profit - Profit = 5 % of the C.P. + 80
5/16 × C.P. - C.P./4 = 5/100 × C.P. + 80
⇒ 5 C.P./16 - C.P./4 - 5 C.P./100 = 80
⇒ 0.3125 C.P. - 0.25 C.P. - 0.05 C.P. = 80
⇒ 0.0125 C.P. = 80
⇒ C.P. = 80/0.0125
∴ Cost Price of the Television = Rs. 6400


Hence, the Cost Price of the Television is Rs. 6400.


Hope it helps.