Question

x:6::5:3 then 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 :-

${\tt \leadsto x : 6 :: 5 : 3}$

Convert both ratios into fractional form.

${\tt \leadsto \dfrac{x}{6} = \dfrac{5}{3}}$

Cross multiply the numbers.

${\tt \leadsto x \times 3 = 5 \times 6}$

Multiply the numbers on RHS.

${\tt \leadsto x \times 3 = 30}$

Shift the number 3 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{30}{3}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = \cancel \dfrac{30}{3} = \pink{\underline{\boxed{\tt x = 10}}}}$

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Verification :-

${\tt \leadsto x : 6 :: 5 : 3}$

Substitute the value of x.

${\tt \leadsto 10 : 6 :: 5 : 3}$

Product of means should be equal to product of extremes.

Product of means :- 6 $\times$ 5 = 30

Product of extremes :- 10 $\times$ 3 = 30

${\tt \leadsto 30 = 30}$

${\tt LHS = RHS}$

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Hence verified !!