Question

A dealer sold a VCR and a TV for RS. \[{\mathbf{38560}}\] making profit of \[{\mathbf{12}}\% \] on VCR and \[{\mathbf{15}}\% \] on TV. By selling them for Rs. \[{\mathbf{38620}}\], he would have realized a profit of \[{\mathbf{15}}\% \] on VCR and \[{\mathbf{12}}\% \] on TV. Find the cost price of each.
A. CP of VCR = Rs. 15000 and CP of TV = Rs. 17000
B . CP of VCR = Rs. 21000 and CP of TV = Rs. 32000
C . CP of VCR = Rs. 18000 and CP of TV = Rs. 16000
D . CP of VCR = Rs. 12000 and CP of TV = Rs. 15000

Answer 1

Hint: As we know that cost price (C.P) means the amount which is paid by the seller to acquire the product and selling price (S.P) is the money that is finally received by the seller after selling that same product to any customer.
If the S.P is more than the C.P then there will be profit and if C.P. is more than the S.P. then there will be loss for the seller.
Hence, Profit% is the percent of profit gained by the seller and loss % is percent of loss suffered by the seller.
Profit and Loss for any product is given by:
[\Profit = S.P - C.P\]
\[Loss = C.P - S.P\]
Now profit and loss percentage can be calculated by:
[\Profit\% = \dfrac{{\Profit}}{{C.P}} \times 100\]
\[Loss\% = \dfrac{{Loss}}{{C.P}} \times 100\]

Complete step by step solution:
Let C.P of VCR be Rs. X, and C.P of TV be Rs. Y.
S.P of VCR\[\, = C.P \times \dfrac{{100 + p}}{{100}}\]
\[\because \]P denotes the profit, and to find out the selling price we use the formula:
\[S.P = C.P \times \left( {\dfrac{{100 + P}}{{100}}} \right)\]
So, the S.P of VCR is \[ = x \times \left( {\dfrac{{100 + 12}}{{100}}} \right)\]\[ = \dfrac{{12}}{{100}}x\]
Selling price of TV \[ = \] C.P of TV \[ \times \,\left( {\dfrac{{100 + p}}{{100}}} \right)\]
\[ = \,y \times \left( {\dfrac{{100 + 15}}{{100}}} \right)\]
\[ = \dfrac{{115}}{{100}}y\]
Given total S.P of VCR and TV is:
\[\dfrac{{112}}{{100}}x + \dfrac{{115}}{{100}}y = 38560\] ________ (1).
By selling them for Rs. \[38620\]then:
\[\dfrac{{115}}{{100}}x + \dfrac{{112}}{{100}}y = 38620\] _________ (2).
Now, we can write equation (1) like this:
\[112x + 115y = 3856000\] _________ (3).
And equation (2)
\[115x + 112y = 3862000\] __________ (4).
In equation (3) we multiply by \[115\]and in equation (4) we multiply by \[112\], we get: -
\[12880x + 13225y = 443,440,000\] ______ (5).
\[12880x + 12544y = 432,544,000\] ______ (6).
Subtraction equation (6) from equation (5):
\[681y = 10896000\]
\[y = 16000\]
Putting the value of y in equation (5) we get:
\[12880x + 13225 \times 1600 = 443,440,000\]
\[12880x + 211,600,000 = 443,440,000\]
\[12880x = 231,840,000\]
\[x = 18000\]
\[\therefore \]C.P of VCR \[ = \]Rs. \[18000\].
C.P of TV \[ = \] Rs. \[16000\]

Note: Cost price calculated by using the formula given below
\[C.P = \dfrac{{100}}{{100 + P\% }} \times S.P\]
C.P means cost price and S.P means selling price, and there would be profit only if S.P \[ > \] C.P.