# Moderate Ratios & Proportion Solved QuestionAptitude Discussion

 Q. Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
 ✖ A. 48 ✔ B. 24 ✖ C. 38 ✖ D. None of these

Solution:
Option(B) is correct

Less Cogs ⇒ more turns and less time ⇒ less turns

Table below can be scrolled horizontally

Cogs Time Turns
A 54 45 80
B 32 8 ?

Number of turns required= $80\times \dfrac{54}{32}\times \dfrac{8}{45}=24\text{ times}$

## (4) Comment(s)

Raj Karan
()

this is the easiest of all

number of cogs are inversely proportional to speed or rotation of the wheels

hence ratio of speeds of two wheels =27/16(27 for smaller cogged wheel)

value of 16 unit given equal to 80

hence 27 unit = 135

in 45 sec 135

in 8 sec =135*8/45 =24

Bushra
()

More explanation req pls..

Deepak
()

I've added a table to the solution, this might be helpful to you.

Suhail
()

We are equating the rate at which it rotates per second,
So we get 80 times per 45 second times number of cogs = x times per 8 seconds times the number of cogs.
54*(80/45)=32*(x/8)

Hope you have got it!