UPSC Prelims 2001 Q145: Science & Technology – Quantitative Aptitude
In 1930, a person’s age was 8 times that of his son. In 1938, the father’s age became ten
times that of his son’s age in 1930. The ages of the son and father in 1940 were, respectively.
- (a) 16 years, 58 years
- (b) 15 years, 50 years
- (c) 14 years, 42 years
- (d) 13 years, 34 years
Answer: (c) 14 years, 42 years
Explanation
Ages of the son and father in 1940
| Year | Son / Father |
|---|---|
| 1930 | s / 8s |
| 1938 | Father = 8s + 8 = 10 × (son's age in 1930) = 10s → s = 4 |
| 1930 ages | Son 4, father 32 |
| 1940 ages | Son 14, father 42 |
Given: in 1930 a person's age was 8 times that of his son, and in 1938 the father's age became ten times the son's age in 1930. So 8s + 8 = 10s, giving s = 4. Adding 10 years for 1940 gives son 14 and father 42.
Answer: (c) 14 years, 42 years.
Why each option is right or wrong
- (a) Incorrect. 16 and 58 do not fit the 1930 ratio of 8 : 1.
- (b) Incorrect. 15 and 50 give 1930 ages of 5 and 40, but 40 + 8 = 48, not 50.
- (c) CORRECT. 1930 ages 4 and 32; 1940 ages 14 and 42.
- (d) Incorrect. 13 and 34 give 1930 ages of 3 and 24, which fail the second condition.
Key point
Age problems: choose the earliest year as the base and add years to every age.
Remember
1930: 4 and 32 → 1940: 14 and 42.
Common mistakes
- Comparing with the son's 1938 age instead of his 1930 age.
- Forgetting to add 10 years for 1940.
- Adding the ten years to only one person.
Exam tip
Read carefully which year each comparison uses.
Sources
- NCERT Class VIII — Mathematics, chapter 'Linear Equations in One Variable'
- R. S. Aggarwal — Quantitative Aptitude, chapter 'Problems on Ages'