Q. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are
a) 45, 80
b) 18, 30
c) 12, 20
d) 15, 25
Correct Answer: d) 15, 25
Question from UPPSC Prelims CSAT 2025
Explanation:
Let the numbers be 3k and 5k. After increasing each by 10, the ratio becomes 5:7.
So, (3k + 10)/(5k + 10) = 5/7 ⇒ 7(3k + 10) = 5(5k + 10) ⇒ 21k + 70 = 25k + 50 ⇒ 20 = 4k ⇒ k = 5.
Thus, the numbers are 3k = 15 and 5k = 25, which matches Option 4.