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# [Smart Math] Ratio Proportion Problem 1

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

A can give B a 30 meters start and C an 80 meters start in a kilometer race. What start can B give to C in the same race?
(1 Kilometer = 1000 meters)

1. 50 meters
2. 61 meters
3. 52 meters
4. 45 meters
5. 40 meters

### The Usual Method

When A travels 1000 meters,

B travels 970 meters and

C travels 920 meters.

Hence, when B has to travel 1000 meters, C will travel $\frac{1000\times 920}{970}$ meters.

This comes from cross multiplication as shown below:

A             B              C

1000     970       920

1000       x

$\therefore x=\frac{1000\times 920}{970}$ = $948\frac{44}{97}$ or 948.45 meters

Therefore B can give a start of 1000 – 948.45 = 51.55 meters $\approx$ 52 meters

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds