View all: RAJSHAHI KRISHI UNNAYAN BANK (SO)| 1$^{st}$ CLASS WRITTEN QUESTION (MATH) SOLVE | 2015
Correct Answer: ans: 35 hours.
Explanation:
The time required for pipe A alone take to fill the tank = 2x $\times$ 2 = 4x hours
C alone can do in 1 hour =$\frac{1}{x}$ part of work
B alone can do in 1 hour =$\frac{1}{2x}$ part of work
A alone can do in 1 hour = $\frac{1}{4x}$part of work
Now, (A + B + C) together can do in 5 hour total 1 work
A + B + C together can do in 1 hour = $\frac{1}{5}$ part of work
According to the question, $\frac{1}{x}$+$\frac{1}{2x}$+$\frac{1}{4x}$ = $\frac{1}{5}$
=> x = $\frac{35}{4}$
The time required for pipe A alone take to fill the tank = 4x = 4 x $\frac{35}{4}$ = 35 hours
Alternative: Suppose pipe A alone takes x hours to fill the tank.
We know, speed and time have inverse relationship and as the pipe C is twice as fast as B and B is twice as fast as A
So, pipes B and C will take $\frac{x}{2}$ and $\frac{x}{4}$ hours respectively to fill the tank.
=> $\frac{1}{x}$+$\frac{2}{x}$+$\frac{4}{x}$ =$\frac{1}{5}$
=> $\frac{7}{x}$ = $\frac{1}{5}$= x = 35
MCQ Shortcut: A,B,C এই তিনজনের একত্রে কাজ = $\frac{ABC}{AB+BC+CA}$
=> 5 = $\frac{(4X)(2X)(X)}{(4x\times 2x)+(2x\times x)(x\times 4x)}$
=> 5 = $\frac{8x}{14}$
=> x = $\frac{35}{4}$
A = 4x = 4 x $\frac{35}{4}$ = 35
