NIFT UG 2010 Question Paper with solutions

Suppose that the incomes of A and B are 5x and 3x respectively and their expenses are 8y and 5y respectively.
Savings of $\mathit{A}=5\mathit{x}\mathit{–}8\mathit{y}$
Savings of $\mathit{B}=3\mathit{x}\mathit{–}5\mathit{y}$
From question,
Savings of A = 36,000 × 2/3 = Rs. 24,000
And Savings of B = 36000 × 1/3 = Rs. 12,000
∴ $5\mathit{x}\mathit{–}8\mathit{y}=24000$ ...(i)
$3\mathit{x}\mathit{–}5\mathit{y}=12,000$.....(ii)
Multiplying Eq. (i) by 3 Eq. (ii) by 5 and subtract (ii) from (i) we get,
$15\mathit{x}\mathit{–}24\mathit{y}=72000$
$15\mathit{x}\mathit{–}25\mathit{y}=60000$
$+$     $-$
––––––––––––––––
    $\mathit{y}=12000$
putting the value of y in Eqn. (ii)
$\therefore \mathit{x}=\frac{12000+60000}{3}=24,000$
∴ Annual income of A $=5\times 24,000$
$=1,20,000$
∴ Monthly income$=\mathrm{Rs}.10,000$