Discussion
Sonu and Monu had some savings in the ratio 4:5. They decided to buy a gift for their mother, sharing the cost in the ratio 3:4. After they bought, Sonu spent two thirds of his amount while Monu was left with ₹ 145. Then the value of the gift is:
Answer: B
The value of the gift is ₹ 140, reading the stem as the key does: Sonu is left with two thirds of his amount.
Let the savings be \(4x\) and \(5x\) and the gift cost \(c\), shared 3:4, so Sonu pays \(\tfrac{3c}{7}\) and Monu \(\tfrac{4c}{7}\). Sonu keeps two thirds of \(4x\), so his share is one third of it:
\[ \begin{aligned} \tfrac{3c}{7} &= \tfrac{4x}{3} \\ c &= \tfrac{28x}{9} \end{aligned} \]
Monu is left with 145:
\[ \begin{aligned} 5x - \tfrac{4}{7}\cdot\tfrac{28x}{9} &= 145 \\ 5x - \tfrac{16x}{9} &= 145 \\ \tfrac{29x}{9} &= 145 \\ x &= 45 \end{aligned} \]
\[ c = \tfrac{28 \times 45}{9} = 140 \]
Check: Sonu has 180 and pays 60, keeping 120, which is two thirds of 180; Monu has 225 and pays 80, keeping 145. The stem as printed says Sonu spent two thirds, which read literally gives no whole-number answer among the options (the share would be 120 and the data inconsistent), so the key only works with the left-with reading. 165, 180 and 185 do not fit either reading.
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