In an examination, 35% of total candidates failed in Hindi, 45% failed in English, and 20% failed in both. Find the percentage of candidates who passed in both subjects.
Total failed = 35 + 45 - 20 = 60%. Percentage passed in both = 100 - 60 = 40%.
Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, how much time will it take to fill the tank?
Combined rate = 1/20 + 1/30 = 5/60 = 1/12 per minute. Time = 12 minutes.
Simplify: $(256)^(0$.16) x $(256)^(0$.09)
$256^(0$.16 + 0.09) = $256^(0$.25) = $256^(1/4)$ = $(4^4$)^(1/4) = 4.
A boat goes 12 km downstream in 48 minutes. If the speed of the current is 2 km/h, what is the speed of the boat in still water?
Downstream speed = 12 km / (48/60 h) = 15 km/h. Boat speed = Downstream speed - Current speed = 15 - 2 = 13 km/h.
The curved surface area of a cylinder of height 14 cm is 88 $cm^2$. Find the diameter of the base of the cylinder. (Take pi = 22/7)
2 * pi * r * h = 88 => 2 * (22/7) * r * 14 = 88 => 88 * r = 88 => r = 1 cm. Diameter = 2 cm.