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__Formulas of Problems on Time and Work - Aptitude Questions and Answers.__

**TIPS FOR SOLVING QUESTIONS RELATED TO TIME AND WORK:**

1. **Still Water:** If the water is not moving then it is called still water.

2. **Stream:** Moving water of the river is called stream.

3. **Downstream:** The direction along the stream is called **downstream**.

4. **Upstream:** The direction opposite the stream is called **upstream**.

5. If the speed of a boat in still water is 'u' km/hr and the speed of the stream is 'v' km/hr, then

\begin{aligned} \text{Speed of boat downstream } = (u + v) km/hr \end{aligned}

\begin{aligned} \text{Speed of boat upstream } = (u - v) km/hr \end{aligned}

6.If the speed downstream is 'a' km/hr and the speed upstream is 'b' km/hr, then

\begin{aligned} \text{Speed of boat in still water } = \frac{1}{2}(a + b) km/hr \end{aligned}

\begin{aligned} \text{Speed of stream } = \frac{1}{2}(a - b) km/hr \end{aligned}

__Shortcut Tips:__

**Tips 1:** A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then
the speed of man in still water is given by

\begin{aligned} = \text{y} \text{(} \frac{t2 + t1}{t2 - t1} \text {)} km/hr \end{aligned}

**Tips 2:** A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes him t hours to row
to a place and come back, then the distance between two places is given by

\begin{aligned} = \frac{t(x^2 - y^2)}{2x} km/hr \end{aligned}

**Tips 3:** A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in
upstream than to go downstream for the same distance, then the distance is given by

\begin{aligned} = \frac{t(x^2 - y^2)}{2y} km/hr \end{aligned}

**Tips 4:** A man can row in still water at x km/h. In a stream flowing at y km/h, if he rows the same distance
up and down the stream, then his average speed is given by

\begin{aligned} = \frac{\text {UpstreamSpeed} * \text {DownstreamSpeed}}{\text {Man's speed in still water}} km/hr \end{aligned}

\begin{aligned} = \frac{(x - y) * (x + y)}{x} km/hr \end{aligned}

\begin{aligned} = \frac{(x^2 - y^2)}{x} km/hr \end{aligned}