SSC & BANK EXAMS: QUANTITATIVE APTITUDE · RATIO & PARTNERSHIP

Problems on ages

Write present ages as ak and bk from the ratio. Both ages change by the same number of years.

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Worked examples

Example 1 · level 1

The ages of Aditya's mother and Aditya are in the ratio 7 : 3, and the sum of their ages is 90 years. What will be Aditya's age after 3 years?

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One part = 90 ÷ (7 + 3) = 9.
Aditya is 3 × 9 = 27 years old now.
After 3 years: 30 years.

Answer: 30 years

Example 2 · level 2

The present ages of Priya's grandfather and Priya are in the ratio 7 : 3. After 9 years the ratio will be 5 : 3. What is the present age of Priya?

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Let the ages be 7k and 3k.
(7k + 9) / (3k + 9) = 5/3 → 3(7k + 9) = 5(3k + 9).
6k = 18 → k = 3.
Present age = 9 years.

Answer: 9 years

Example 3 · level 3

3 years ago, the ratio of the ages of Tenzin's father and Tenzin was 9 : 2. 14 years from now, the ratio will be 5 : 3. What is the present age of Tenzin?

Show solution

Let the present ages be x (father) and y (Tenzin).
(x − 3) : (y − 3) = 9 : 2 and (x + 14) : (y + 14) = 5 : 3.
Solving the two linear equations gives x = 21, y = 7.
Check: 18 : 4 = 9 : 2 and 35 : 21 = 5 : 3.

Answer: 7 years