Question

In a city the number of shops and the number of restaurants are in the ratio 1 :2

the number of restaurants and the number of pubs are in the ratio 8 :3
There are 30 pubs in the city.
How many shops are there in the city?

Answer 1

40 shops

Explanation:

To combine the ratios, we must have the same number of ratio units for restaurants. We can get that by multiplying the first ratio by 4.

S : R = 1 : 2 . . . multiplying by 4 gives . . . 4 : 8

and

R : P = 8 : 3

So, the extended ratio can be written ...

S : R : P = 4 : 8 : 3

Multiplying this by 10 gives 30 for the number of pubs:

S : R : P = 40 : 80 : 30

The number of shops in the city is 40.