Equal addition changing a ratio – UGC NET Question

Let the numbers be 4x and 7x. After adding 5 to each, they become 4x + 5 and 7x + 5, and their ratio is given as 3:5. Thus (4x + 5)/(7x + 5) = 3/5. Cross multiplying gives 5(4x + 5) = 3(7x + 5), which simplifies to 20x + 25 = 21x + 15, and hence x = 10. Therefore the numbers are 40 and 70, and the larger original number is 70.

Option A:
Option A, 40, is the smaller of the two original numbers when x = 10. It satisfies the initial ratio but does not answer the question, which specifically asks for the larger number. Moreover, choosing 40 as the larger number would contradict the ratio 4:7 where 4x must be smaller than 7x.

Option B:
Option B, 45, does not fit into any pair maintaining both the original ratio 4:7 and the new ratio 3:5 after adding 5. If we treated 45 as the larger original number, then the smaller would be 45 × (4/7), which is not an integer and fails the requirement for simple integer ratio terms. Thus 45 is an inconsistent choice.

Option C:
Option C is correct because 70 arises naturally as 7 × 10 when solving the given proportion. Substituting 40 and 70 back into the problem, we get (40 + 5):(70 + 5) = 45:75 = 3:5, which verifies the condition. This confirms that 70 is the true larger original number.

Option D:
Option D, 75, would require the smaller number to be 75 × (4/7) ≈ 42.86 to preserve the original ratio, which is not an integer and also fails to give the new ratio 3:5 after adding 5. Therefore 75 does not satisfy the structural requirements of the problem.