Question

Which of the following are in proportion: (a) 21, 35, 24, 40
(b) 5, 7, 40, 64

Answer 1

Hint: Firstly calculate the extreme values and the middle terms. Then calculate their product separately and verify the formula of proportion that is product of extremes should be equal to product of middle terms.

Formula used: Here formula will be used product of extremes = product of middle terms.

Complete step-by-step answer:
21, 35, 24, 40
Extreme numbers are 21 and 40 whereas middle terms are 35 and 24.
By using the formula (product of extremes = product of middle terms.)
We will verify whether the left hand side is equal to the right hand side or not.
While calculating left hand side that is product of extremes values which is equal to:
\[ \Rightarrow 21 * 40\]
\[ \Rightarrow 840\]
So, product of extreme come out to be: 840
While calculating right hand side that is product of middle values which is equal to:
\[ \Rightarrow 24 * 35\]
\[ \Rightarrow 840\]
So, product of middle terms come out to be: 840
Hence it is verified that the left hand side is equal to the right hand side. i.e product of extremes = product of middle terms=840 .
5, 7, 40, 64
Extreme numbers are 5 and 64 whereas as middle terms are 7 and 40.
 By using the formula (product of extremes = product of middle terms.)
We will verify whether the left hand side is equal to the right hand side or not.
 While calculating left hand side that is product of extremes values which is equal to:
 \[ \Rightarrow 5 * 64\]
\[ \Rightarrow 320\]
So, product of extreme come out to be: 320
While calculating right hand side that is product of middle values which is equal to:
\[ \Rightarrow 7 * 40\]
\[ \Rightarrow 280\]
So, product of middle terms come out to be: 280
Hence it is verified that the left hand side is not equal to the right hand side. i.e product of extremes \[ \ne \] product of middle terms.
So, option (a) 21, 35, 24, 40 is in proportion.

Note: In these types of questions we must follow some steps like we should try to find out extreme values and the middle terms. Then we should calculate the product's extreme and middle terms. Therefore we can check that the numbers are in proportion or not.