Question

Divide 180 into three parts with a ratio of 2:3:4

Answer 1

★ How to do :-

Here, we are given with a number 180 that should be divided in three parts. We are given with the ratio of division of the number between three parts. The ratio given is 2:3:4. We are just asked to find out that, how much numbers will each of the three people get. So, we can find the numbers obtained to each each easily. We need some other concepts to solve this question. The concepts used here are the variables and the transposition of numbers from one hand side to the other. This process changes the sign of a particular number. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 2 : 3 : 4 = 180}$

Insert a variable x to each parts of ratio and add them.

${\tt \leadsto 2x + 3x + 4x = 180}$

Add all the values on LHS.

${\tt \leadsto 9x = 180}$

Shift the number 9 from LHS to RHS.

${\tt \leadsto x = \dfrac{180}{9}}$

Simplify the fraction on RHS to get the value of x.

${\tt \leadsto x = 20}$

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Number obtained to first person :-

${\tt \leadsto 2x = 2 \times 20}$

Multiply the values to get the answer.

${\tt \leadsto 40}$

Number obtained to second person :-

${\tt \leadsto 3x = 3 \times 20}$

Multiply the values to get the answer.

${\tt \leadsto 60}$

Number obtained to third person :-

${\tt \leadsto 4x = 4 \times 20}$

Multiply the values to get the answer.

${\tt \leadsto 80}$

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${\red{\underline{\boxed{\bf So, \: the \: numbers \: obtained \: are \: 40, \: 60 \: and \: 80 \: respectively.}}}}$