Question

The sum of two numbers, one of which is two-thirds of the other, is 45. Find the smaller number.

Answer 1

Answer:

18 is smaller number.

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Answer 2

$\large\underline{\sf{Given- }}$

The sum of two numbers, one of which is two-thirds of the other, is 45.

$\purple{\large\underline{\sf{To\:Find - }}}$

The smaller number.

$\green{\large\underline{\sf{Solution-}}}$

Given that,

The sum of two numbers, one of which is two-thirds of the other, is 45.

Let assume that

$\rm :\longmapsto\:First \: number = x$

$\rm :\longmapsto\:Second \: number = \dfrac{2}{3}x$

So, numbers are

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number = x} \\ \\ &\sf{Second \: number = \dfrac{2}{3}x } \end{cases}\end{gathered}\end{gathered}$

According to statement

$\rm :\longmapsto\:x + \dfrac{2}{3}x = 45$

$\rm :\longmapsto\: \dfrac{3x + 2x}{3} = 45$

$\rm :\longmapsto\: \dfrac{5x}{3} = 45$

$\rm :\longmapsto\:x = 45 \times \dfrac{3}{5}$

$\rm :\longmapsto\:x = 9 \times 3$

$\bf\implies \:x = 27$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{First \: number = x = 27} \\ \\ &\sf{Second \: number = \dfrac{2}{3}x = \dfrac{2}{3} \times 27 = 18 } \end{cases}\end{gathered}\end{gathered}$

Verification

First number = 27

Second number = 18

So, Sum = 27 + 18 = 45

Second number = 2/3 × 27 = 18

Hence, Verified

So, Smaller number = 18