Question
Anjali,' 'Bheem,' and 'Chetna' started a business
together with initial investments of Rs. 3,875, Rs. (B + 2700), and Rs. 'B,' respectively. After 16 months, 'Bheem' reduced his investment by half, and 'Chetna' increased his investment by Rs. 900. If the ratio of the profit received by 'Bheem' and 'Chetna' after 3 years is 26:25, respectively, then find the difference between the initial investments made by 'Anjali' and 'Chetna.'Solution
ATQ, Let the initial investment of ‘Chetna’ = Rs.‘2a’ Then, initial investment of ‘Bheem’ = Rs.(2a + 2700) Investment of ‘Bheem’ after 16 months = (2a+ 2700)/2 = Rs. (a + 1350) Investment of ‘Chetna’ after 16 months = Rs.(2a + 900) Ratio of profit shares of ‘Bheem’ to that of ‘Chetna’ = [(2a + 2700) × 16 + (a + 1350) × 20]:[(2a × 16) + (2a + 900) × 20] = 26:25 Or, (8a + 10800 + 5a + 6750):(8a + 10a + 4500) = 26:25 Or, (13a + 17550) × 25 = (18a + 4500) × 26 Or, 325a + 438750 = 468a + 117000 Or, 321750 = 143a Or, a = 2250 So, initial investment of ‘Chetna’ = 2a = Rs. 4500 Difference between initial investments of ‘Anjali’ and ‘Chetna’ = 4500 – 3875 = Rs.625
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