Question

The difference between two whole number is 66. The ratio of these number is 2:5 then smaller number is

Answer 1

Given: The Difference b/w two whole numbers is 66. & the ratio of these two whole numbers is 2: 5.

Need to find: The Smaller number?

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⌑ Let's say, that the smaller number be 2x and greater number be 5x respectively.

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Given that,

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• It is given that, difference b/w these two whole numbers is 66.

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$:\implies\frak{ Greater\;no. - Smaller\;no. = Difference}\\\\\\:\implies\frak{ 5x - 2x = 66}\\\\\\:\implies\frak{ 3x = 66}\\\\\\:\implies\frak {x = \cancel\dfrac{66}{3}}\\\\\\:\implies{\pmb{\underline{\boxed{\purple{\frak{x = 22}}}}}}\;\bigstar$

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Therefore,

• Smaller number, 2x = 2(22) = 44
• Greater number, 5x = 5(22) = 110

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$\therefore{\underline{\textsf{Hence, the smaller number is \textbf{44}.}}}$

$\rule{230px}{.2ex}$

• V E R I F I C A T I O N :

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• As We know that, the difference between the two whole numbers is 66. So, Let's Verify answer —

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$:\implies\sf 5x - 2x = 66$

$:\implies\sf 5(22) - 2(22) = 66$

$:\implies\sf 110 - 44 = 66$

$:\implies{\pmb{\underline{\boxed{\frak{66=66}}}}}$

$\quad\quad\quad\quad\therefore{\underline{\pmb{\mathcal{HENCE\; VERIFIED!}}}}$

Answer 2

Answer:

Given :-

• The difference between two whole number is 66.
• The ratio of these number is 2 : 5.

To Find :-

• What is the smaller number.

Solution :-

Let,

$\mapsto \bf First\: Number =\: 2a$

$\mapsto \bf Second\: Number =\: 5a$

$\bigstar$ The difference between the whole number is 66.

Hence, according to the question,

$\implies \sf 5a - 2a =\: 66$

$\implies \sf 3a =\: 66$

$\implies \sf a =\: \dfrac{\cancel{66}}{\cancel{3}}$

$\implies \sf a =\: \dfrac{22}{1}$

$\implies \sf\bold{\purple{a =\: 22}}$

Hence, the required numbers are :

❒ First Number :

$\longrightarrow \sf First\: Number =\: 2a$

$\longrightarrow \sf First\: Number =\: 2(22)$

$\longrightarrow \sf First\: Number =\: 2 \times 22$

$\longrightarrow \sf\bold{\red{First\: Number =\: 44}}$

❒ Second Number :

$\longrightarrow \sf Second\: Number =\: 5a$

$\longrightarrow \sf Second\: Number =\: 5(22)$

$\longrightarrow \sf Second\: Number =\: 5 \times 22$

$\longrightarrow \sf\bold{\red{Second\: Number =\: 110}}$

Here, we can observed that the smaller number is 44.

${\small{\bold{\underline{\therefore\: The\: smaller\: number\: is\: 44\: .}}}}$

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$\large{\boxed{\underline{\underline{\bf{VERIFICATION\: :-}}}}}$

$\leadsto \tt{5a - 2a =\: 66}$

By putting a = 22 we get,

$\leadsto \tt{5(22) - 2(22) =\: 66}$

$\leadsto \tt{110 - 44 =\: 66}$

$\leadsto \tt{\bold{\pink{66 =\: 66}}}$

$\rightarrow \sf\bold{\green{L.H.S =\: R.H.S}}$

Hence, Verified.