A man spend 25% of his salary on food, 10% of his salary on maintenance his house, 5% in...
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A man spend 25% of his salary on food, 10% of his salary on maintenance his house, 5% in children education, 10% on petrol, and 30% in his entertainment and rest he put in his savings.
Now in the next year his salary is increased by 20% but his expenses also increased on food by 2%, on maintenance by 1%, on petrol by 1% and on entertainment it is increased by 2%. If the difference in the savings in both the year is Rs. 3232. Then find the current salary of the man.
Show answer & explanation
Year 1 savings = 20% of salary. Year 2 salary increases by 20%, but total expenses increase by only 6% (weighted average), resulting in higher savings. The difference of Rs. 3232 corresponds to a current salary of Rs. 101000.
Step-by-step Derivation:
Year 1: Let salary = S. Expenses = 25% + 10% + 5% + 10% + 30% = 80%. Savings = 20% of S = 0.2S.
Year 2: New salary = 1.2S. Expense percentages become: Food 27%, Maintenance 11%, Education 5%, Petrol 11%, Entertainment 32% = 86% of new salary. Savings = 14% of 1.2S = 0.168S.
Wait—recalculating: Year 2 expenses increase by absolute percentage points (not percentage of new salary). Year 2 total expenses = (25+2)% + (10+1)% + 5% + (10+1)% + (30+2)% = 86% of new salary. Savings Year 2 = 14% of 1.2S = 0.168S.
Difference = 0.168S − 0.2S = −0.032S. This is negative, so reconsider: expenses as absolute increases to percentages. Year 2 savings = 1.2S × 0.14 = 0.168S. Year 1 savings = 0.2S. Difference = 0.2S − 0.168S = 0.032S = 3232. Therefore S = 3232 / 0.032 = 101000.