Question : 65% of Samita's income is equal to 91% of Bhairav's income. If Samita's income was INR 1,500 more than what it is and Bhainav's income was INR 500 more than what it is, the ratio of the incomes of Samita and Bhairav would have been 3 : 2. What is the actual combined income (in INR) of Samita and Bhairav?
Option 1: 18,500
Option 2: 17,500
Option 3: 20,000
Option 4: 18,000
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Correct Answer: 18,000
Solution :
Let the income of Samita and Bhairav be $x$ and $y$ respectively.
According to the question,
$65\%\text{ of }x=91\%\text{ of }y$
⇒ $\frac{65}{100}\text{ of }x=\frac{91}{100}\text{ of }y$
⇒ $65x=91y$
⇒ $x=\frac{91}{65}y$..............(1)
Also according to the question,
$(x+1500):(y+500)=3:2$
⇒ $\frac{x+1500}{y+500}=\frac{3}{2}$
⇒ $2(x+1500)=3(y+500)$
⇒ $2x+3000=3y+1500$
⇒ $3y-2x=1500$
Putting value $x$ from equation (1), we get,
⇒ $3y-2(\frac{91}{65}y)=1500$
⇒ $\frac{195y-182y}{65}=1500$
⇒ $13y=1500\times 65$
⇒ $y=\frac{1500\times 65}{13}$
⇒ $y=1500\times 5=\small\text{INR}$ $7500$ [Bhairav's Income]
Also, $x=\frac{91}{65}=\frac{91}{65}\times 7500=\small\text{INR}$ $10500$ [Samita's Income]
⇒ Combined income of Samita and Bhairav = INR 10,500 + INR 7,500 = INR 18,000
Hence, the correct answer is 18,000.
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