If a man’s present age is twice what it was 10 years ago, what is his current age?
- (a)20
- (b)30
- (c)40
- (d)25
Answer
Why
Correct — A.
Rule: call the present age x, so the age 10 years ago is x − 10.
Set up: x = 2(x − 10)
Expand: x = 2x − 20
Subtract x from both sides: 20 = x
Present age = 20
Check: 10 years ago he was 10, and 20 = 2 × 10 → option (a).
Why the others are wrong
- (b)30 — 30 means he was 20 ten years ago. Double 20 is 40, not 30, so the condition fails.
- (c)40 — 40 means he was 30 ten years ago. Double 30 is 60, so 40 fails the condition.
- (d)25 — 25 means he was 15 ten years ago. Double 15 is 30, not 25.
Concept
Age problems become one equation once you name the unknown. Let the present age be x. Ten years ago it was x − 10.
'Present age is twice the age 10 years ago' becomes x = 2(x − 10), and solving gives x = 20.
A shortcut: the gap between the two ages is always 10. If the present age is double the past age, that gap equals the past age, so he was 10 and is now 20.
Key facts
- A person's age now and n years ago always differ by n.
- If present age = k × (age n years ago), then present age = k × n ⁄ (k − 1).
- With k = 2 and n = 10: 2 × 10 ⁄ 1 = 20.
Study next
Common traps
- Writing the equation the wrong way round, 2x = x − 10, which gives a negative age
- Using x + 10 for the past age, which also gives a negative answer
24 Sep 2024, 12:30, Quant Q.2 uses the same x − 10 step for two people: Ghanshyam is three times Akash's age now and was four times it 10 years ago, keyed a difference of 60.
23 Sep 2024, 09:00, Quant Q.1 adds a future condition for Sunita and Tanya, keyed 7 : 3.
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