A boat goes 16 km upstream and 24 km downstream in 6 hours. It also goes 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water. MCQ with Answer and Explanation

Let speed in still water = x, stream = y. 16/(x-y) + 24/(x+y) = 6; 12/(x-y) + 36/(x+y) = 6. Let 1/(x-y)=a, 1/(x+y)=b. 16a+24b=6, 12a+36b=6. Solving: a=1/4, b=1/12. So x-y=4, x+y=12 → x=8, y=4. Wait, x=8, not 10. I miscalculated: 16a+24b=6, divide by 2: 8a+12b=3. 12a+36b=6 → 2a+6b=1. From 2a+6b=1 → a=(1-6b)/2. Substitute: 8*(1-6b)/2 +12b = 4(1-6b)+12b = 4-24b+12b = 4-12b = 3 → b=1/12. Then a = (1-6/12)/2 = (1-0.5)/2 = 0.25 = 1/4. So x-y=4, x+y=12 → x=8. So answer 8 kmph. Option B 8 kmph. I'll correct options.