The monthly income of a person was Rs.13, 500 and his monthly expenditure was Rs.9000. Next year's income increased by 14% and his expenditure increased by 7%. The percentage increase in his savings was: $ (a){\text{ 7% }} \\ (b){\text{ 21% }} \\ (c){\text{ 28% }} \\ (d){\text{ 35% }} \\ $
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Hint – In this question the new monthly income will be previously monthly income + 14% of previous monthly income, similarly the new monthly expenditure will be previous monthly expenditure + 7% previous monthly expenditure. Use the concept that saving is equal to income – expenditure.
Complete step-by-step answer: Monthly income of a person = Rs. 13,500. His monthly expenditure was = Rs. 9,000. So the saving of the person is the difference of monthly income and monthly expenditure. Therefore saving = 13,500 – 9,000 = Rs. 4,500. Now next year his income has increased by 14%. Therefore his new monthly income = previous monthly income + 14% of previous monthly income Therefore his new monthly income = $13500 + \dfrac{{14}}{{100}} \times 13500 = 15390$ Rs. Now next year his monthly expenditure has increased by 7%. Therefore his new monthly expenditure = previous monthly expenditure + 7% of previous monthly expenditure. Therefore his new monthly expenditure = $9000 + \dfrac{7}{{100}} \times 9000 = 9630$ Rs. So the new savings of the person is the difference of new monthly income and new monthly expenditure. Therefore new monthly saving = 15,390 – 9,630 = Rs. 5,760. So the increase in saving = new monthly saving – previous monthly saving. So the increase in saving = 5,760 – 4,500 = Rs. 1,260 So the percentage increase in saving is the ratio of increase in the saving to the previous monthly saving multiplied by 100. Therefore % increase in monthly saving = $\dfrac{{1260}}{{4500}} \times 100$ Therefore % increase in monthly saving = 28%. So this is the required percentage increase in the monthly saving. Hence option (C) is correct.
Note – In this question previously the person has certain income and certain monthly expenditure, so the savings could be calculated, now in next year his monthly income along with the expenditure gets increased. So saving will be changed accordingly so the percentage increase in saving is the ratio of increase in the saving to the previous monthly saving multiplied by 100 so substitute the values and simplify it we will get the required answer.