One says; “Give me a hundred rupees, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten rupees, I shall be six times as rich as you.” What is the amount of their (respective) capital?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹40, ₹170
Let the first friend have a and the second b. The first statement gives a + 100 = 2(b − 100), that is a = 2b − 300. The second gives b + 10 = 6(a − 10), that is b = 6a − 70.
Substituting, a = 2(6a − 70) − 300 = 12a − 440, so 11a = 440 and a = 40; then b = 170. Checking: 40 + 100 = 140 = 2 × 70, and 170 + 10 = 180 = 6 × 30.