Question
Determine the combined savings of 'Arvind' and 'Bishma'
if 'Bishma' has savings equal to one-third of 'Arvind's expenditure, while 'Arvind' earns a salary twice the amount of 'Bishma's expenditure. Additionally, 'Bishma's salary is Rs. 3,000 more than 'Arvind's savings. Given that the total expenditures of 'Arvind' and 'Bishma' amount to Rs. 7,500, calculate the total savings of both individuals.Solution
ATQ, We can say that the salary of ‘Arvind’ be Rs. ‘2a’ Expenditure of ‘Bishma’ = 2a ÷ 2 = Rs. ‘a’ Let the expenditure of ‘Arvind’ be Rs. ‘3b’ savings of ‘Bishma’ = 3b ÷ 3 = Rs. ‘b’ ATQ, 2a – 3b + 3000 = a + b Or, 3000 = 4b – a ………… (I) Also, a + 3b = 7500 …………… (II) On adding equation (I) and (II), we have; 7b = 10500 Or, b = 1500 Putting b = 1500 in equation (I), we have Or, a = 4 × 1500 – 3000 So, a = 3000 Savings of ‘Bishma’ = 1500 Savings of ‘Arvind’ = 2a – 3b = 2 × 3000 – 3 × 1500 = 1500 Hence required sum = 1500 + 1500 = Rs. 3,000
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