Question
Income of Riya is Rs. (124n + 1680). She spends 75% of
her income and saves the rest. Savings of her friend Mehul is Rs. 960 more than that of her. Mehul saves 50% of his income. If average expenditure of Riya and Mehul is Rs. (74n - 360). Which of the following statement(s) is/are true? I. 'n' is less than the square of 12 II. (n - 41) is a perfect square III. Sum of each digit of 'n' is 5Solution
Expenditure of Riya = 0.75 × (124n + 1680) = Rs. (93n + 1260)
Savings of Riya = 124n + 1680 - 93n - 1260 = Rs. (31n + 420)
Savings of Mehul = 31n + 420 + 960 = Rs. (31n + 1380)
Income of Mehul = (31n + 1380) ÷ 0.5 = Rs. (62n + 2760)
Expenditure of Mehul = 62n + 2760 - 31n - 1380 = Rs. (31n + 1380)
(93n + 1260 + 31n + 1380) ÷ 2 = 74n - 360
Or, 124n + 2640 = 148n - 720
Or, 62n + 1320 = 74n - 360
Or, 12n = 1680
Or, 'n' = 140
Statement I:
Square of 12 = 144
140 < 144
So, statement I is true.
Statement II:
140 - 41 = 99, which is not a perfect square
So, statement II is false.
Statement III:
Required sum = 1 + 4 + 0 = 5
So, statement III is true.
Therefore, statements I and III are true.
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