CAT 2020 Quant Question [Slot 2] with Solution 11

Let the price of each pencil be Rs. \(x\) and price of each sharpens be Rs. y

Aron \(y - x = 2\quad  \Rightarrow \quad \therefore x = y - 2\)

\(a(y - 2) + b(y) = 2a(y - 2) + (b - 10)y\)

\(10y = a(y - 2) \to (1)\)

Required value \( = 3a\)

From \((1)\quad a = \frac{{10y}}{{y - 2}}a \in {I^ + }\)

Its possible only when \(y = 22\)

\(\therefore a = 11\)

Required answer =33