Question

On selling a TV at 5% gain and a fridge at 10% gain, a shopkeeper gains Rs 3250. But, if he sells TV at 10% gain and the fridge at 5% loss, he gains Rs 1500. Find the actual cost price of TV and that of the fridge.

Answer 1

Let the cost price of the TV be Rs. x and the cost price of the fridge be Rs. y.
Then, we have:
When the gain on the TV is 5%:
Rs. $\left(5\%\mathrm{of}x\right)$ = Rs. $\left(\frac{5x}{100}\right)$ = Rs. $\left(\frac{x}{20}\right)$
When the gain of the fridge is 10%:
Rs. $\left(10\%\mathrm{of}y\right)$ = Rs. $\left(\frac{10y}{100}\right)$ = Rs. $\left(\frac{y}{10}\right)$
Given:
Gain on the TV and the fridge = Rs. 3250
Rs. $\left(\frac{x}{20}\right)$ + Rs. $\left(\frac{y}{10}\right)$ = Rs. 3250
⇒ $\left(\frac{x+2y}{20}\right)=3250$
⇒ (x + 2y) = 65000 ....(i)

Again, we have:
When the gain on the TV is 10%:
Rs. $\left(10\%\mathrm{of}x\right)$ = Rs. $\left(\frac{10x}{100}\right)$ = Rs. $\left(\frac{x}{10}\right)$
When the loss on the fridge is 5%:
Rs. $\left(5\%\mathrm{of}y\right)$ = Rs. $\left(\frac{5y}{100}\right)$ = Rs. $\left(\frac{y}{20}\right)$
Gain on the TV and the fridge = Rs. 1500
Rs. $\left(\frac{x}{10}\right)$ − Rs. $\left(\frac{y}{20}\right)$ = Rs.1500
⇒ $\left(\frac{2x-y}{20}\right)=1500$
⇒ (2x − y) = 30000 ....(ii)
On multiplying (ii) by 2, we get:
4x − 2y = 60000 ....(iii)
On adding (i) and (iii), we get:
5x = 125000
⇒ x = 25000
On substituting x = 25000 in (i), we get:
25000 + 2y = 65000
⇒ 2y = 40000
⇒ y = 20000
Hence, the cost price of the TV is Rs. 25000 and the cost price of the fridge is Rs. 20000.