Question
A mixture contains (d + 24) litres of petrol and oil in
a 3:5 ratio. To this, 40 litres of oil and (d - 72) litres of petrol are added, altering the ratio to 2:3 for petrol to oil. Based on this information, which of the following statements could be correct? I. Given the stream's speed is 7 km/hr and the boat's speed in calm water is 8 km/hr, the boat takes 8 hours to travel (d + 16) km downstream. II. When 5582 is divided by (d + 4), the remainder is 72. III. (d + 21) is a perfect square.Solution
We can say that Quantity of petrol in initial mixture = (d + 24) × [3/(3 + 5)] = (3d + 72)/8 Quantity of oil in initial mixture = (d + 24) × [5/(3 + 5)] = (5d + 120)/8 ATQ, [{(3d + 72)/8} + (d – 72)]/[{(5d + 120)/8} + 40] = 2/3 Or, [(3d + 72) + 8d – 576]/[5d + 120 + 320] = 2/3 Or, (11d – 504)/(5d + 440) = 2/3 Or, 33d – 1512 = 10d + 880 Or, d = 104 From I: Distance = 104 + 16 = 120 km Time taken by boat in downstream = 120/(8 + 7) = 8 hours So, ‘I’ is true. From II: Number = 104 + 4 = 108 5582/108 = 108 × 51 + 74 Remainder = 74 So, ‘II’ is false. For III: √(104 + 21) = √125 = 11.180 So, (x + 21) is not a perfect square. So, ‘III’ is false.
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