Two numbers are in the ratio 3 : 5. If 4 is subtracted from each of these two numbers, the new numbers then are in the ratio 4 : 7. Find the smaller of the two original numbers.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 36
Let the two numbers be 3x and 5x, where x is a positive constant.
When 4 is subtracted from each of the numbers, the new numbers become 3x - 4 and 5x - 4.
We are given that the new numbers are in the ratio 4 : 7. Therefore, we can write:
(3x - 4)/(5x - 4) = 4/7
Cross-multiplying, we get:
7(3x - 4) = 4(5x - 4)
Simplifying, we get:
21x - 28 = 20x - 16
x = 12
Therefore, the two original numbers are 3x = 36 and 5x = 60.
The smaller of the two original numbers is 36