Question
Income of Aakash is 66⅔% more than the expenditure of
Bhavya. Income of Bhavya is 25% more than the expenditure of Aakash. If savings of Bhavya is Rs. 4,600 more than that of Aakash and ratio between expenditure and savings of Aakash is 6:1, respectively, then find the income of Bhavya.Solution
Let the expenditure of Bhavya be Rs. ‘3x’
So, income of Aakash = 3x × (5/3) = Rs. ‘5x’
Let the expenditure of Aakash be Rs. ‘4y’
So, income of Bhavya = 4y × (5/4) = Rs. ‘5y’
So, savings of Aakash = 4y × (1/6) = Rs. (2y/3)
ATQ;
5x – 4y = (2y/3)
Or, 5x = (14y/3)
Or, x = (14y/15)
Since, savings of Bhavya is Rs. 4,600 more than that of Aakash.
5y – 3x = (2y/3) + 4600
On putting x = (14y/15):
5y – 42y/15 = 2y/3 + 4600
Or, 11y/5 = 2y/3 + 4600
Or, (33y – 10y)/15 = 4600 ⇒ 23y/15 = 4600
So, y = 3000
So, income of Bhavya = 5 × 3000 = Rs. 15,000
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