Question

A wheel that has 12 cogs is meshed with a larger wheels of 24 cogs. When the smaller wheel has made 40 revolutions, the number made by the larger wheel is:
A)22
B)16
C)20
D)18

Answer 1

The number of revolutions made by the larger wheel is 20

Given :

• A wheel that has 12 cogs is meshed with a larger wheels of 24 cogs.

• The smaller wheel has made 40 revolutions

To find :

The number of revolutions made by the larger wheel

Solution :

Step 1 of 2 :

Form the equation to find the number of revolutions made by the larger wheel

The number of cogs in smaller wheel = 12

The number of cogs in larger wheel = 24

Now it is given that the smaller wheel has made 40 revolutions

Let number of revolutions made by the larger wheel = x

Now , number of cogs is inversely proportional to the number of revolution of a wheel

By the given condition

$\displaystyle \sf 12 : 24 = x : 40$

Step 2 of 2 :

Calculate the number of revolutions made by the larger wheel

$\displaystyle \sf 12 : 24 = x : 40$

$\displaystyle \sf{ \implies } \frac{12}{24} = \frac{x}{40}$

$\displaystyle \sf{ \implies }24x = 12 \times 40$

$\displaystyle \sf{ \implies }x = \frac{12 \times 40}{24}$

$\displaystyle \sf{ \implies }x = 20$

So number of revolutions made by the larger wheel is 20

Hence the correct option is C) 20

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