Question

Are 21,24,35,44 in proportiin ? If not what should be the fourth term for which they will be in proportion?

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

They are not in Proportion.

To make it a Proportion, the forth terms should be 40.

$\textbf{\underline{\underline{Explanation :- }}}$

Given :

The numbers = 21,24,35,44

To find :

Are the Given numbers in Proportion, if not then what should be the fourth term for which they will be in proportion.

Solution :

Proportion = 21 : 24 : : 35 : 44

$\star$As we know :

$\boxed{\sf{Mean \times Mean \: terms = Extreme \times Extreme \: terms}}$

Mean Terms : 24 and 35

Extreme Terms : 21 and 44

LHS =

$\sf{\implies}$ 24 × 35

$\sf{\implies}$ 840

LHS = 840

RHS =

$\sf{\implies}$ 21 × 44

$\sf{\implies}$ 924

RHS = 924

$\sf{840 \: \not = 924}$

${\boxed{\sf\:{LHS \not= RHS }}}$

$\therefore$ They are not in Proportion.

To make it a Proportion, the 4th term should be =

Consider the 4 term as x

Mean Terms = 25 and 35

Extreme Terms = 21 and x

$\sf{\implies}24 \times 35 = 21 \times x$

$\sf{\implies}840 = 21x$

$\sf{\implies}x = \dfrac{840}{21}$

$\sf{\implies}x = 40$

${\boxed{\bigstar{\sf\:{Fourth \: term = 40}}}}$

$\therefore$ The 4th term should be 40 to make it a Proportion.

$\textbf{\underline{\underline{Verification :-}}}$

$\sf{\implies}24 \times 35 = 21 \times 40$

$\sf{\implies}840 = 840$

When we placed the value of x (40) we got the required answer 840.

$\therefore$ The 4th term should be 40 to make it a Proportion.