Question
A tank has three pipes, X, Y, and Z. X can fill the tank
in 8 hours, Y can fill it in 12 hours, and Z can empty it in 6 hours. If X, Y, and Z are opened together, how long will it take to fill the tank?Solution
Work done by X in 1 hour = 1/8 Work done by Y in 1 hour = 1/12 Work done by Z in 1 hour (emptying) = -1/6 Net work in 1 hour = (1/8) + (1/12) - (1/6) Taking LCM of 8, 12, and 6 = 24, Net work = (3/24) + (2/24) - (4/24) = 1/24 The tank will be filled in 24 hours.
If p = 24 - q - r and pq + r(q + p) = 132, then find the value of (p² + q² + r²).
((99.9 - 20.9)² + (99.9 + 20.9)² )/(99.9 x 99.9 + 20.9 x 20.9) = ?
...
Find the value of the given expression-
(4x+4 -5× 4x+2) / 15×4x – 22×4x
If 4x² + y² = 40 and x y = 6, then find the value
of 2x + y?
If p = 40 - q - r and pq + r(q + p) = 432, then find the value of (p² + q² + r²).
47.98 × 4.16 + √325 × 12.91 + ? = 79.93 × 5.91
If x + y = 4 and (1/x) + (1/y) = 24/7, then the value of (x3 + y3).
- If p = 20 - q - r and pq + r(p + q) = 154, then find the value of (p² + q² + r²).
If a = (√2 - 1)1/3, then the value of (a-1/a)3 +3(a-1/a) is:
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