A family income is Rs.35,000 in a month. The family spends the income on various expenditures, viz., food, health, education, entertainment, and rent. After incurring all the expenditures, 8% is saved every month. The expenditure on health is 50% more than that of food. While food is three times of the expenditure on entertainment, the expenditure on health is half of the expenditure on education. The expenditure on rent is onethird of the combined expenditure on food, health and education. How much expenditure (in Rs.) is incurred on education?
This questions was previously asked in
ssc cgl 2023 pre
Explanation:
Correct option is 1- Rs. 12,600
Given a monthly family income of Rs. 35,000, with 8% savings, the total monthly expenditure amounts to Rs. 32,200.
Breakdown of Expenditures:
Savings:
- Savings = 8% of Rs. 35,000 = Rs. 2,800
- ?Total Expenditure = Rs. 35,000 - Rs. 2,800 = Rs. 32,200
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Expenditure Relationships:
- Let the expenditure on entertainment be EEE.
- Expenditure on food = 3E3E3E
- Expenditure on health = 50% more than food = 1.5×3E=4.5E1.5 \times 3E = 4.5E1.5×3E=4.5E
- Expenditure on education = twice health = 2×4.5E=9E2 \times 4.5E = 9E2×4.5E=9E
- Expenditure on rent = one-third of the sum of food, health, and education = 13×(3E+4.5E+9E)=13×16.5E=5.5E\frac{1}{3} \times (3E + 4.5E + 9E) = \frac{1}{3} \times 16.5E = 5.5E31?×(3E+4.5E+9E)=31?×16.5E=5.5E
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Total Expenditure:
- Total = Food + Health + Education + Entertainment + Rent
- Total = 3E+4.5E+9E+E+5.5E=23E3E + 4.5E + 9E + E + 5.5E = 23E3E+4.5E+9E+E+5.5E=23E
- Given Total Expenditure = Rs. 32,200
- Thus, 23E=32,20023E = 32,20023E=32,200
- Solving for EEE:
- E=32,20023E = \frac{32,200}{23}E=2332,200?
- E=1,400E = 1,400E=1,400
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Expenditure on Education:
- Education = 9E=9×1,400=Rs. 12,6009E = 9 \times 1,400 = Rs. 12,6009E=9×1,400=Rs. 12,600
Therefore, the expenditure incurred on education is Rs. 2,600.
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By: Parvesh Mehta