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प्रश्न
On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹ 7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains ₹ 13. Find the actual price of each of the tea set and the lemon set.
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उत्तर
Given: Let the cost price of the tea-set = ₹ x and the lemon-set = ₹ y.
When tea is sold at 5% loss and lemon at 15% gain, net gain = ₹ 7.
When tea is sold at 5% gain and lemon at 10% gain, net gain = ₹ 13.
Step-wise calculation:
1. Case I (5% loss on tea, 15% gain on lemon):
Loss on tea = 5% of x = `x/20`.
Gain on lemon = 15% of y = `(3y)/20`.
Net gain = `(3y)/20 - x/20 = 7`
⇒ 3y – x = 140 ...(Equation 1)
2. Case II (5% gain on tea, 10% gain on lemon):
Gain on tea = `x/20`.
Gain on lemon = `y/10`.
Total gain = `x/20 + y/10 = 13`
⇒ x + 2y = 260 ...(Equation 2)
3. Solve (1) and (2):
From (1): x = 3y – 140
Substitute into (2):
(3y – 140) + 2y = 260
⇒ 5y – 140 = 260
⇒ 5y = 400
⇒ y = 80
Then x = 3(80) – 140
= 240 – 140
= 100
Cost price of the tea-set = ₹ 100 and cost price of the lemon-set = ₹ 80.
