Question

if
$\frac{3}{5}$
of a number exceeds its
$\frac{2}{7}$
by 44 ,
find the number..​

Answer 1

Solution :-

Let the number be x.

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3/5 of x = 3x/5

2/5 of x = 2x/5

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According To Question :-

$\rightarrow{\sf{\dfrac{3x}{5} = \dfrac{2x}{7} + 44}}$

$\rightarrow{\sf{\dfrac{3x}{5} - \dfrac{2x}{7} = 44}}$

$\rightarrow{\sf{\dfrac{21x - 10x}{35} = 44}}$

$\rightarrow{\sf{\dfrac{11x}{35} = 44}}$

$\rightarrow{\sf{ x = \dfrac{44 \times 35}{11}}}$

$\rightarrow{\boxed{\sf{ x = 140}}}$

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Hence,

$\boxed{\boxed{\sf{The\ number\ is\ 140.}}}$

Answer 2

• $\dfrac{3}{5}$ of a number exceeds its $\dfrac{2}{7}$ by 4.

_______ [GIVEN]

We have to find the number.

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» Let the number be M.

Given numbers = $\dfrac{3}{5}$ and $\dfrac{2}{7}$

We let number M. So, now numbers are..

$\dfrac{3M}{5}$ and $\dfrac{2M}{7}$

» $\dfrac{3M}{5}$ of a number exceeds (increase means plus) it's $\dfrac{2M}{7}$ by 44.

• A.T.Q.

=> $\dfrac{3M}{5}$ = 44 + $\dfrac{2M}{7}$

=> $\dfrac{3M}{5}$ - $\dfrac{2M}{7}$ = 44

LCM of 5 and 7 is 35.

=> $\dfrac{21M\:-\:10M}{35}$ = 44

=> $\dfrac{11M}{35}$ = 44

=> 11M = 44 × 35

=> 11M = 1540

=> M = $\dfrac{1540}{11}$

=> M = 140.

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We have to find number. And we let the number be M.

________________________________

So, the number is 140.

__________ [ANSWER]

✡ $\dfrac{3M}{5}$ = 44 + $\dfrac{2M}{7}$

Put M = 140

=> $\dfrac{3\:\times\:140}{5}$ = 44 + $\dfrac{2\:\times\:140}{7}$

=> $\dfrac{420}{5}$ = 44 + $\dfrac{280}{7}$

=> 84 = 44 + 40

=> 84 = 84

___________ [HENCE VERIFIED]