Question

help me im stuck on this question for the past hour
1:3::4:x

Answer 1

★ How to do :-

Here, we are given with three numbers and also a variable 'x'. We are asked to find the value of the variable x. Here, we can apply two methods in which the value of x can be found. We can find the value of x by converting the ratios in fractional form, and then cross multiply them to find the value of x. Thr other method is to multiply the means and also the extremes of a proportion separately. If they are same, we can consider that four numbers can form a proportion. So, let's solve!!

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➤ Solution :-

Method 1 :-

${\tt \leadsto 1 : 3 :: 4 : x}$

Multiply the means.

Product of means :- ${\tt 3 \times 4 = 12}$

Product of extremes :- ${\tt 1 \times x = 12}$

${\tt \: \: \: \: \: \: \: \: \: x = \dfrac{12}{1} = 12}$

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Method 2 :-

${\tt \leadsto 1 : 3 :: 4 : x}$

Convert each ratio into fraction.

${\tt \leadsto \dfrac{1}{3} = \dfrac{4}{x}}$

Cross multiply the numbers.

${\tt \leadsto 1 \times x = 3 \times 4}$

Multiply the numbers on LHS and RHS.

${\tt \leadsto 1x = 12}$

Shift the number 1 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{12}{1} = 12}$

$\Huge\therefore$ The value of x is 12.