The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is?Options30 years32 years35 years33 years
Question
The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is?Options30 years32 years35 years33 years
Solution
Let's solve this step by step:
Step 1: Let's assume the present ages of A and B are 5x and 6x respectively.
Step 2: According to the problem, after 7 years, the ratio of their ages becomes 6 : 7. So, we can write it as (5x + 7) / (6x + 7) = 6 / 7.
Step 3: Cross multiply to solve for x. We get 7*(5x + 7) = 6*(6x + 7).
Step 4: Simplify this to get 35x + 49 = 36x + 42.
Step 5: Rearrange to find the value of x. We get x = 49 - 42 = 7.
Step 6: Substitute x = 7 in the expression for A's age. We get A's age = 5x = 5*7 = 35 years.
So, the present age of A is 35 years.
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