With the amount he received as a return on investment from equities, Dinesh planned to buy a few home accessories on sale. He bought a fan and a carriage worth Rs. 3000. Later his friend got the same fan and carriage from Dinesh, Dinesh sold the carriage at a loss of 20% and the fan with a profit of 25%. In this overall transaction, Dinesh gained exactly 6 percent. What would have been the cost of the fan Dinesh bought? (approximately)
Question
With the amount he received as a return on investment from equities, Dinesh planned to buy a few home accessories on sale. He bought a fan and a carriage worth Rs. 3000. Later his friend got the same fan and carriage from Dinesh, Dinesh sold the carriage at a loss of 20% and the fan with a profit of 25%. In this overall transaction, Dinesh gained exactly 6 percent. What would have been the cost of the fan Dinesh bought? (approximately)
Solution
Let's denote the cost of the fan as F and the cost of the carriage as C. We know from the problem that F + C = 3000.
Dinesh sold the carriage at a loss of 20%, so he sold it for 0.8C. He sold the fan at a profit of 25%, so he sold it for 1.25F.
The problem states that Dinesh gained exactly 6 percent in the overall transaction. This means that the total amount he received from selling the fan and the carriage is 1.06 times the total amount he spent on them. So, we have the equation:
1.25F + 0.8C = 1.06(F + C)
Substituting F + C = 3000 into this equation gives:
1.25F + 0.8(3000 - F) = 1.06 * 3000
Solving this equation for F gives the cost of the fan that Dinesh bought.
Let's solve it:
1.25F + 2400 - 0.8F = 3180 0.45F = 780 F = 780 / 0.45 F = Rs. 1733.33 (approximately)
So, the cost of the fan Dinesh bought was approximately Rs. 1733.33.
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