Question

Ratio between two number 3:6 their sum 144 find the number

Answer 1

Answer:

16×3 =48

16×6=96 sum is 144= 96+48

Answer 2

Step-by-step explanation:

Analysis :-

$\: \: \: \:$ In this question we're given with the ratio of two numbers and their sum. And, we're asked to find out the numbers, respectively.

• Ratio of the numbers is 3 : 6.
• The sum of the numbers is 144.

Understanding The Concept :-

$\: \: \: \:$ To find the numbers, firstly, let us assume the value of first number be "3x". So that the value of the second number will be "6x", since the ratio of the numbers is 3 : 6.

As through the given data provided in the question, we know that the sum of the two numbers is 144, hence the equation so formed is,

$\: \: \: \: \: \: \: \: \: \: \: \: \: {\underbrace{\boxed{\sf{3x\ +\ 6x\ =\ 144}}}_{\tiny\blue {\sf{Required\ equation}}}}$

Solution :-

$\: \: \: \:$ By solving the equation, we can obtain the value of "x". After having the value of x, we will confirm the value of x by verifying it. And to get the numbers, we simply put the value of x in the assumed numbers, and will get our final numbers. Let's do it !

Calculations :-

➲ Finding the value of x :

$\: \: \: \:$ This calculation can be carried out by solving our required equation, that is, 3x + 6x = 144.

$\tt \longmapsto {3x\ +\ 6x\ =\ 144} \\ \\ \sf \longmapsto {9x\ =\ 144} \\ \\ \sf \longmapsto {x\ =\ \dfrac{144}{9}} \\ \\ \sf \longmapsto {x\ =\ \dfrac{\cancel 3 \times 48}{\cancel 3 \times 3}} \\ \\ \sf \longmapsto {x\ =\ \dfrac{\cancel {48}}{\cancel {3}}} \\ \\ {\underbrace{\boxed{\sf{\pink{x\ =\ 16}}}}_{\tiny\blue {\sf{Value\ of\ x}}}}$

Now, we've the value of x, that is, 16. So, before proceeding to the next step in finding the numbers, let us confirm the value of x by verifying it.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ ✦ Verification ✦

$\tt \longmapsto {3x\ +\ 6x\ =\ 144} \\ \\ \sf \longmapsto {3(16)\ +\ 6(16)\ =\ 144} \\ \\ \sf \longmapsto {3 \times 16\ +\ 6 \times 16\ =\ 144} \\ \\ \sf \longmapsto {48\ +\ 96\ =\ 144} \\ \\ {\underbrace{\boxed{\sf{\pink{144\ =\ 144}}}}_{\tiny\blue {\sf{Hence,\ Verified}}}}$

Now, the value of x is verified as the LHS is equal to the RHS. Hence, the value of x is correct.

$\: \: \: \:$ Now, we'll find out the numbers. This can be done by substituting the value of x in the assumed numbers.

➲ Finding numbers :

$\tt \longmapsto {1^{st}\ number\ =\ 3x} \\ \\ \sf \longmapsto {3(16)} \\ \\ \sf \longmapsto {3 \times 16} \\ \\ {\underbrace{\boxed{\sf{\red{48}}}}_{\tiny\blue {\sf{First\ number}}}}$

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$\tt \longmapsto {2^{nd}\ number\ =\ 6x} \\ \\ \sf \longmapsto {6(16)} \\ \\ \sf \longmapsto {6 \times 16} \\ \\ {\underbrace{\boxed{\sf{\red{96}}}}_{\tiny\blue {\sf{Second\ number}}}}$

By solving the formed equation we get the numbers as 48 and 96. Hence, the required numbers are 48 and 96 respectively.