Question : The monthly income of a family is Rs. 35,000. The family spends the income on various expenses, viz., food, health, education, entertainment, and rent. After incurring all the expenses, they save 8% every month. The expenditure on health is 50% more than that of food. While food is three times the expenditure on entertainment, the expenditure on health is half of the expenditure on education. The expenditure on rent is one-third of the combined expenditure on food, health, and education. How much expenditure (in Rs.) is incurred on education?
Option 1: Rs. 12,600
Option 2: Rs. 8,400
Option 3: Rs. 13,200
Option 4: Rs. 7,700
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Correct Answer: Rs. 12,600
Solution :
A family income is Rs 35,000 in a month.
8% is saved every month.
So, monthly expenditure $=\frac{35000×92}{100}=32200$
Let's assume they spend 100 on food.
So, their health expenditure = (100 + 50) = 150
Their entertainment expenditure = $\frac{100}{3}$
Their education expenditure = (2 × 150) = 300
So, the rent expenditure = $\frac{1}{3}×(100+150+300)=\frac{550}{3}$
Total expenditure $=(100+150+\frac{100}{3}+300+\frac{550}{3})=(\frac{2300}{3})$
So, when $(\frac{2300}{3})$ is total expenditure, education expenditure is 300.
Therefore, when 32,200 is the total expenditure, then the expenditure on education is $(300×\frac{3}{2300}×32200)$ = Rs. 12,600
Hence, the correct answer is Rs. 12,600.
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