CAT 2017 Set-1 | Question: 71

Question

Ravi invests $50\%$ of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs $59500$, then Ravi's total monthly savings (in Rs) is

• A. $71000$
• B. $63000$
• C. $50000$
• D. $70000$

Answer 1

Let Ravi’s total monthly saving be ₹ $x.$

• Ravi’s Invested in fixed deposits $ = \frac{50}{100}\times x = \frac{x}{2} $
• Ravi’s rest savings $ =  x- \frac{x}{2} = \frac{x}{2}$
• Ravi Invested in stocks $ = \frac{30}{100}\times\frac{x}{2} = \frac{3x}{20}$
• Ravi’s saving bank account $ =  \left(\frac{x}{2} – \frac{3x}{20}\right) = \frac{7x}{20}$

Total amount deposited by him in the bank (for the savings account and the fixed deposits) $ =  \frac{7x}{20}  + \frac{x}{2}$

$\Rightarrow \frac{17x}{20} = 59500$

 $\Rightarrow  \boxed{ x = ₹\;70000}.$

---

$\textbf{Short Method:}$ Let Ravi’s total monthly saving be ₹ $100.$

• Ravi’s Invested in fixed deposits $ = \frac{50}{100}\times 100 = 50 $
• Ravi’s rest savings $ =  100-50 = 50$
• Ravi Invested in stocks $ = \frac{30}{100}\times 50 = 15$
• Ravi’s saving bank account $ =  50-15 = 35$

Total amount deposited by him in the bank (for the savings account and fixed deposits) $ = 35 + 50$

• $85 \longrightarrow 59500$
• $100 \longrightarrow \dfrac{59500}{85} \times 100 = ₹\;70000.$

Correct Answer $:\text{D}$