Question

On selling a tea-set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains Rs. 13. Find the actual price of the tea set and the lemon set:

• A. Tea set: Rs. 180, Lemon Set: Rs. 120
• B. Tea set: Rs. 130, Lemon Set: Rs. 70
• C. Tea set: Rs. 90, Lemon Set: Rs. 100
• D. Tea set: Rs. 100, Lemon Set: Rs. 80

Answer 1

Answer: (D)

Let the cost of the tea set = x and the cost of lemon set = y
If he sells a tea set at 5% loss and lemon set at 15% gain
$\Rightarrow lossonateaset=x\times \frac{5}{100}$
$\Rightarrow gainonlemonset=y\times \frac{15}{100}$
$\Rightarrow \frac{15}{100}y-\frac{5}{100}x=7$
$\Rightarrow 15y-5x=700$
$\Rightarrow -x+3y=140\left(i\right)$
If he sells a tea set at 5% gain and the lemon set at 10 % gain, total gain = 13Rs
$\Rightarrow \frac{5}{100}x+\frac{10}{100}x=13$
$\Rightarrow 5x+10y=1300...\left(ii\right)$
Now multiplying eq 1 from 5 and adding eq 2 will get
$\Rightarrow -5x+15y=700$
$\Rightarrow 5x+10y=1300$
$\Rightarrow 25y=2000$
$\Rightarrow y=80$
Now putting y = 80 in eq 1 will get
$\Rightarrow -x+3\times 80=140$
$\Rightarrow -x+240=140$
$\Rightarrow -x=-100$
$\Rightarrow x=100$
Hence actual price of tea set = 100 and actual price of lemon set = 80