Kamla and Savitri are aged in the ratio 6 : 5, and the sum of their present ages is 44 years. What will be the ratio of their ages after 8 years?

Introduction / Context: This problem uses an age ratio with a known sum to find present ages, and then asks for the ratio after a fixed time increment. It reinforces basic ratio partitions and linear updates to ages.

Given Data / Assumptions:

• Kamla : Savitri = 6 : 5.
• Sum of present ages = 44 years.
• Find the ratio after 8 years.

Concept / Approach: If 6x + 5x = 44, then x is the basic unit of age. Compute each age, then add 8 years to both and simplify the resulting ratio.

Step-by-Step Solution: 6x + 5x = 44 ⇒ 11x = 44 ⇒ x = 4. Kamla = 6x = 24 years; Savitri = 5x = 20 years. After 8 years: Kamla = 32, Savitri = 28. Required ratio = 32 : 28 = 8 : 7.

Verification / Alternative check: The sum remains consistent when adding the same number to both. The simplified ratio 8 : 7 directly results from dividing 32 and 28 by 4.

Why Other Options Are Wrong: 5 : 6 and 7 : 8 invert or misstate the direction. 14 : 13 is not equivalent to 8 : 7 and does not come from the computed ages.

Common Pitfalls: Forgetting to simplify the final ratio or miscomputing x from the sum 44. Always check by multiplication back to 44.

Final Answer: 8 : 7