Question
Income of Raghav is Rs. (80n + 1200). He spends 75% of
his income and saves the rest. Savings of his friend Mohit is Rs. 1,200 more than that of him. Mohit saves 40% of his income. If average expenditure of Raghav and Mohit is Rs. (50n - 675). Which of the following statement(s) is/are true? I. 'n' is greater than cube of largest single digit prime number II. (n - 306) is a perfect square III. Sum of each digit of 'n' is 9Solution
Expenditure of Raghav = 0.75 X (80n + 1200) = Rs. (60n + 900) Savings of Raghav = 80n + 1200 - 60n - 900 = Rs. (20n + 300) Savings of Mohit = 20n + 300 + 1200 = Rs. (20n + 1500) Income of Mohit = (20n + 1500) ÷ 0.4 = Rs. (50n + 3750) Expenditure of Mohit = 50n + 3750 - 20n - 1500 = Rs. (30n + 2250) (60n + 900 + 30n + 2250) ÷ 2 = 50n - 675 Or, 90n + 3150 = 100n - 1350 Or, 10n = 4500 Or, 'n' = 450 Statement I: Largest single digit prime number = 7 7³ = 343 < 450 So, statement I is true. Statement II: 450 - 306 = 144, which is a perfect square So, statement II is true. Statement III: Required sum = 4 + 5 + 0 = 9 So, statement III is true. Therefore, all statements I, II and III are true.
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