Question

There are 70 vehicle in a piece of land. If there are a total number of 200 tyres in the land how many cars and bikes were there in the land??

Answer 1

Answer:

40 bikes and 30 cars

Step-by-step explanation:

Assuming that there are only cars and bikes.

Total no. of vehicles = 70

Total no. of tyres = 200

When we divide 200 by 70, we get $2 \frac{6}{7}$ as the answer. This is considered as the average.

We know that a car has 4 tyres and a bike has 2 tyres.

Find the difference between the average and the no. of tyres (4 and 2) each by subtracting from the largest.

4 - $2 \frac{6}{7}$ = $1 \frac{1}{7} = \frac{8}{7}$

$2 \frac{6}{7}$ - 2 = $\frac{6}{7}$

Now write these differences as ratio.

$\frac{8}{7} : \frac{6}{7} = 8 : 6 = 4 : 3$

This 4 : 3 ratio is the ratio of no. of bikes to no. of cars.

See it carefully. The ratio is bike to car, not car to bike!

Now find the no. of cars and bikes each.

As there are a total of 70 vehicles, this is divided in the ratio 4 : 3.

No. of bikes = $70 \times \frac{4}{7} = \bold{40}$

No. of cars = $70 \times \frac{3}{7} = \bold{30}$

∴ There are 40 bikes and 30 cars.

Let's check.

Total no. of vehicles

= 40 + 30 = 70

Total no. of tyres

= (40 × 2) + (30 × 4) = 80 + 120 = 200

So it's right.

Hope this may be helpful.

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