Discussion
Shalini's mother is 12 years more than twice of Shalini's age. After 8 years, she will be 20 years less than three times of Shalini's age. Then the age of Shalini's mother is :
Answer: A
Shalini's mother is 44 years old.
Let Shalini's present age be \(s\). Then the mother's age is \(2s + 12\). After 8 years the mother is 20 years less than three times Shalini's age then:
\[ \begin{aligned} 2s + 12 + 8 &= 3(s + 8) - 20 \\ 2s + 20 &= 3s + 4 \\ s &= 16 \end{aligned} \]
So the mother is \(2 \times 16 + 12 = 44\) years. Check: in 8 years she will be 52 and Shalini 24, and \(3 \times 24 - 20 = 52\).
46, 48 and 50 do not satisfy both conditions; for example 48 would make Shalini 18, and then in 8 years 56 is not \(3 \times 26 - 20 = 58\).
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