The average monthly expenditure of a family was ₹10,000 during the first three months, ₹12,500 during the next four months, and ₹13,500 during the last five months of a year. If the total savings during the year was ₹32,500, then 70% the average monthly income of the family (in ₹) was:
As we know,
$$Average\ =\frac{Sum\ of\ observation}{Number\ of\ observation}$$
Given,
i.e; Total expenditure of 3 months = $$₹10000\times\ 3=₹30000$$
i.e; Total expenditure of 4 months = $$₹12500\times\ 4=₹50000$$
i.e; Total expenditure of 5 months = $$₹13500\times\ 5=₹67500$$
Total expenditure of a year = ₹30000 + ₹50000 + ₹67500 = ₹147500
Total saving of that year = ₹32500 (given)
We know,
Total income = Total Expenditure + Total Saving
i.e; ₹147500 + ₹32500 = ₹180,000
Montly Income = $$\frac{₹180000}{12}=₹15000$$
70% of monthly Income = $$\frac{70}{100}\times\ 15000=₹10500$$
Hence, Option D is correct.
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