Question

Amit sold a jacket at 8% gain. Had it been sold for Rs 75 more, the gain would have been 14%.
Find the cost price of the jacket.
[Hint: Find S.P. at the jackets at 8% and 14% gains then apply gives conditions.]​

Answer 1

The answer is =Rs.1350.

Hope it helps.

Answer 2

Given:

Gain on the jacket is 8%

To find:

The cost price of the jacket.

Solution:

Let us denote the selling price by X and the cost price by Y.

We know that the gain % is,

Gain% = $(\frac{Gain}{C.P})$ × 100

Gain = S.P- C.P

S.P is the selling price

C.P is the cost price

From the above two formulas, we get the formula of gain% in terms of the selling price.

S.P = $(\frac{100 + gain percent }{100} )$ × C.P.

X  = $(\frac{100+8}{100} )$ × Y

X= $(\frac{108}{100} )$ Y

X = (27/25)Y                                ( equation 1 )            

With a rise of Rs.75 in the selling price, the gain becomes 14%.

New selling price = X + 75

New gain % = 14%

X + 75 =  $(\frac{100+14}{100} )$ × Y

X + 75 = (114/100) Y

X + 75 = (57/50) Y                       (equation 2 )

Solving the two equations by putting the value of X from equation one in equation 2, we get,

$\frac{27Y}{25}$ + 75 = $\frac{57Y}{50}$

$\frac{57Y}{50} - \frac{27Y}{25} = 75$                            ( equation 3 )

Solving the equation 3, we get,

Y = 1250

The cost price of the jacket is Rs. 1250.