Problem 1 - Entrance Test

Let their present ages be 7k and 8k. Three years ago: (7k−3)/(8k−3)=4/5. Cross-multiplying gives 35k−15=32k−12 → 3k=3 → k=1. Sum is 7k+8k=15k=15 years. Wait, this contradicts options. Correction: If 3k=3, k=1, sum=15. But this discrepancy suggests an error in calculations. Let’s re-express: 35k−15=32k−12 → 3k=3 → k=1. Sum is 15. However, the provided options are higher. Rechecking the problem setup: Let present ages be 7x and 8x. Three years ago: (7x−3)/(8x−3)=4/5 → 35x−15=32x−12 → 3x=3 → x=1. Sum=15. But this contradicts the options. Therefore, the problem must have incorrect initial setup. Let’s instead solve using variables: Let 3 years ago X =4m, Y=5m. Present ages: 4m+3 and 5m+3. Their present ratio is (4m+3)/(5m+3)=7/8. Cross-multiplying: 32m+24=35m+21 → 3=3m → m=1. Present ages are 4(1)+3=7 and 5(1)+3=8. Sum=15. This still conflicts with options. The correct answer must be missing due to a calculation error in options. Therefore, the problem is ill-conceived. A valid problem would have x=... but for this case, the correct sum is 15, though not listed here.