 ## What is Ratio ?

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six which is equivalent to 4:3.

## Try this Problem from AMC 10B – 2020 – Problem No.-3

The ratio of w to x, y to z and z to x are 4:3, 3:2 and 1:6 respectively . What is the ratio of w to y ?

A) 4:3 B) 3:2 C) 8:3 D) 4:1 E) 16 :3

Source
Competency
Difficulty
Suggested Book

American Mathematics Competition 10 (AMC 10B), 2020, Problem Number 3

Ratio

3 out of 10

Mathematics can be fun

## Use some hints

First hint

This one is an easy sum to solve but those who are confused right now can use the first hint :

The ratio of w : x = 4 : 3 ; so we can write it $\frac {w}{x} = \frac {4}{3}$. Similarly we can do it for the other given ratios. Try to do it……

Second Hint

I think you have already got the answer . If not then try this out …..

z : x = 1 : 6 i.e $\frac {z}{x} = \frac {1}{6}$

y : z = 3 : 2 i.e $\frac {y}{z} = \frac {3}{2}$

Final Step

This hint is the final hint as already mentioned in header :

Lets multiply each ratios :

$\frac {w}{x} \times \frac {x}{z} \times \frac {z}{y} = \frac {4}{3} \times 6 \times \frac {2}{3}$

After canceling out all the similar terms $\frac {w}{y} = \frac {16}{3}$