Q. Mrs. Lata was 3 times as old as her son 8 years ago. Their total age is 64 years now. How old (in years) is Mrs. Lata now?
✅ Correct Answer: (D)
44
Explanation: Suppose present age of Mrs. Lata = P years
Present age of son = Q years
∴ Their total age = 64 years
P + Q = 64 ....... (i)
According to question,
8 years ago , present age of Mrs. Lata - 8 years = 3 × ( present age of her son - 8 years )
⇒ P – 8 = 3 (Q – 8)
⇒ P – 8 = 3Q – 24
⇒ P – 3Q = – 16 ......(ii)
From equations (i) and (ii), we get
4Q = 80 ⇒ Q = 20
Putting the value of Q in eq.(i)
∴ Age of Mrs. Lata = 64 – 20 = 44 years
Explanation by: Mr. Dubey
Suppose present age of Mrs. Lata = P years
Present age of son = Q years
∴ Their total age = 64 years
P + Q = 64 ....... (i)
According to question,
8 years ago , present age of Mrs. Lata - 8 years = 3 × ( present age of her son - 8 years )
⇒ P – 8 = 3 (Q – 8)
⇒ P – 8 = 3Q – 24
⇒ P – 3Q = – 16 ......(ii)
From equations (i) and (ii), we get
4Q = 80 ⇒ Q = 20
Putting the value of Q in eq.(i)
∴ Age of Mrs. Lata = 64 – 20 = 44 years
Present age of son = Q years
∴ Their total age = 64 years
P + Q = 64 ....... (i)
According to question,
8 years ago , present age of Mrs. Lata - 8 years = 3 × ( present age of her son - 8 years )
⇒ P – 8 = 3 (Q – 8)
⇒ P – 8 = 3Q – 24
⇒ P – 3Q = – 16 ......(ii)
From equations (i) and (ii), we get
4Q = 80 ⇒ Q = 20
Putting the value of Q in eq.(i)
∴ Age of Mrs. Lata = 64 – 20 = 44 years