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Quantity B: There are 28 students in a hostel. If the number of students is increased by 12, the expenses of the mess increased by Rs. 92 per day. While the average expenditure per head decreased by Rs. 1. Find per week original expenses of the mess.1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B |
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Answer» Quantity A: Suppose the numbers are x, y and Z; ⇒ (x + y)/2 + z = 36---- 1 ⇒ x + (y + z)/2 = 30---- 2 ⇒ (x + z)/2 + y = 26---- 3 These equations can be written as x + y + 2z = 72 2x + y + z = 60 x + z + 2y = 52 Adding the equations ⇒ 4 (x + y + z) = 184 ⇒ (x + y + z) = 46---- 4 From equation 1, 2, 3 and 4 ⇒ x = 14, y = 6, z = 26 ∴ Product of the numbers = 14 × 6 × 26 = 2184 Quantity B: Suppose the original per head EXPENSE of the mess was Rs. a According to the given condition ⇒ 28a + 92 = 40(a – 1) ⇒ 12a = 132 ⇒ a = 11 ∴ Per week original expenses of the mess = 7 × 28 × 11 = 2156 ∴ Quantity A > Quantity B |
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