Ajay bought two tables for ₹5400. He sold one at a loss of 5% and the other at a gain of 7%. If there is no profit no loss in the whole transaction, then what are the costs of the two tables?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹3150, ₹2250
There is no profit and no loss in all, so the loss on the first table equals the gain on the second.
Assuming the first table cost ₹x and the second ₹(5400 − x):
Loss on the first \(=\) gain on the second: \(0.05x=0.07(5400-x)\)
\(5x=7(5400-x)\), so \(12x=37800\)
\(x=3150\); the second table cost \(5400-3150=2250\)
Shortcut: Equal amounts at 5% and 7% need the costs in the inverse ratio 7 : 5. Splitting 5400 in the ratio 7 : 5 gives \(\frac{7}{12}\times5400=3150\) and \(\frac{5}{12}\times5400=2250\).