Question

a dealer sold A VCR and a TV for RS 38560 making a profit of 12 percent on CVR and 15 percent on TV .by selling them for rs 38620 ,he would have realised a profit of 15 percent on CVR and 12percent on TV. find the cost price of each

Answer 1

Answer :

Let Cost price of VCR = x
And
Cost price of TV = y
So,
From first condition , we get

x + 12% of x + y + 15% of y = 38560

$$\begin{gathered} \Rightarrow x+\frac{12x}{100}+y+\frac{15y}{100}=38560 \\ \Rightarrow x+\frac{3x}{25}+y+\frac{3y}{20}=38560 \\ \Rightarrow \frac{28x}{25}+\frac{23y}{20}=38560 \\ \Rightarrow \frac{112x+115y}{100}=38560 \\ \mathbf{\Rightarrow }\mathbf{112}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{115}\mathit{y}\mathbf{=}\mathbf{}\mathbf{}\mathbf{3856000}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{(}\mathbf{}\mathbf{1}\mathbf{}\mathbf{)} \end{gathered}$$

And

From second condition , we get


x + 15% of x + y + 12% of y = 38620

$$\begin{gathered} \Rightarrow x+\frac{15x}{100}+y+\frac{12y}{100}=38620 \\ \Rightarrow x+\frac{3x}{20}+y+\frac{3y}{25}=38620 \\ \Rightarrow \frac{23x}{20}+\frac{28y}{25}=38620 \\ \Rightarrow \frac{115x+112y}{100}=38620 \\ \mathbf{\Rightarrow }\mathbf{115}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{112}\mathit{y}\mathbf{=}\mathbf{}\mathbf{}\mathbf{3862000}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{}\mathbf{(}\mathbf{}\mathbf{2}\mathbf{}\mathbf{)} \end{gathered}$$

Now we multiply by 115 in equation 1 and 112 in equation 2 , we get

12880 x + 13225 y = 4434400 ----- ( 3 )
And
12880 x + 12544 y = 4325440 ------ ( 4 )

Subtract equation 4 from equation 3 , we get

681 y = 108960

y = 160 , Substitute that value in equation 1 , we get

112 x + 115 ( 160 ) = 38560

112 x + 18400 = 3856000

112 x = 3856000 - 18400

112 x = 3837600

x = $\frac{3837600}{112}$

x = 34264.28

So,

Cost of VCR = Rs. 34264.28
And
Cost of TV = Rs . 160 ( Ans )