Working With Percentages When there is a Zero In The Equation

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

10 April 2005

Peter Maingi asks: if a company makes a loss of sh100,000 in one year and then manages to just break-even (zero profit) in the following year, what is the percentage increase in earnings? What if it made a profit of sh100,000 in the second year?

To get the answer, let us first work with a simpler question: if you earn sh100 and then your salary is raised to sh120, what is the percentage increase? 20 percent, of course! We arrive at that answer by first subtracting the final salary (sh120) from the initial (sh100), then we divide the difference by the starting pay (i.e., sh20 divided by sh100), and finally we multiply that fraction (0.2) by 100 per cent.

In Maingi’s problem, the starting point is negative sh100,000 (loss of sh100,000) and the final value is zero. If we go through the above process with these new figures, we get – zero minus negative sh100,000 equals positive sh100,000; sh100,000 divided by negative sh100,000 equals negative one; therefore the increase is minus100 percent. QED.

In the same way, the answer to the second question comes to negative 200 percent. Let me now throw back the puzzle to Maingi: what if in the first year the company made zero profit and then a sh100,000 loss in the second year, what is the percentage drop in earnings?

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Mike Wanjala wants to know what falls faster, a heavy object or a light one. Ideally, all objects fall at the same rate – I am hesitant to say “same speed” because the velocity constantly increases as the object falls. That being the case, why does a stone fall faster than a piece of paper?

The answer is air resistance. Since paper is light, its motion is easily slowed down by the air. The magnitude of this breaking depends largely on two factors, namely, the density of the object (mass per unit volume) and the surface area exposed to the direction of motion. This explains how a parachute works.

The paratrooper jumps off an aeroplane with the parachute folded into a compact bundle on his back. At the right moment, he opens it thus creating a large surface area. This increases the breaking force and slows him down to a safe landing speed.

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Finally, many readers have asked this one: Which is faster, a bus moving at 80km/h or a car moving at 80km/h? The answer is none; they both have the same speed. The expectation that the bus will be faster since it has larger wheels is false.

The figure indicated by the speedometer is not the speed of the wheels but that of the vehicle – the number of kilometres it will cover in one hour if it maintains that velocity. However, if you fitted a car with the wheels of a bus (not an easy task!) and the speed shown on its Speedo was 80km/h, it would be faster than a bus also showing 80km/h on its gauge.

Thus you can make your car go faster by fitting lager wheels, but this would be at the expense of power output, fuel consumption and the vehicle’s stability.