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Question

The downstream speed of a boat is 48 km/hr, while its upstream speed is 32 km/hr. The boat takes 10 hours to travel a distance of (p + 40) km downstream and (q + 60) km upstream. Additionally, it takes 13 hours to travel (p + 56) km upstream and (q + 140) km downstream. Determine the value of (p + q).

A 450 Correct Answer Incorrect Answer
B 250 Correct Answer Incorrect Answer
C 320 Correct Answer Incorrect Answer
D 300 Correct Answer Incorrect Answer
E none of these Correct Answer Incorrect Answer

Solution

ATQ, (p + 40)/48 + (q + 60)/32 = 10 (2p + 80 + 3q + 180)/96 = 10 2p + 3q = 960 – 260 = 700 … (i) Also, (p + 56)/32 + (q + 140)/48 = 13 (3p + 168 + 2q + 280)/96 = 13 3p + 2q = 1248 – 448 3p + 2q = 800 … (ii) Solving equation, (i) and (ii), we get, p = 200 and q = 100 Hence, required sum = (p + q) = 200 + 100 = 300

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