Question

one third of a number exceeds one seventh of the number by 16.find the number

Answer 1

the number is -84..

equation:

Let the required no. be 'f'.

:. 1/3f +16 = 1/7f

    1/3f - 1/7f = -16

    4f/21 = -16

     4f = -16*21

    4f= -336

    f= -336/4

    :. f = -84
 
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Answer 2

Answer:

The number is 84

Step-by-step explanation:

Given:

One-third of a number exceeds one-seventh of the number by 16

Find:

The number = ?

Solution:

Given that, one-third of a number exceeds one-seventh of the number by 16.

Let the number be '$x$'

One-third of the number = $\frac{1}{3} \times x = \frac{x}{3}$

One-seventh of the number = $\frac{1}{7} \times x = \frac{x}{7}$

Now, $\frac{x}{3}$ exceeds $\frac{x}{7}$ by 16. That is,

$\frac{x}{3} = \frac{x}{7}+16$

⇒ $\frac{x}{3} = \frac{x+(16\times 7)}{7}$

⇒ $\frac{x}{3} = \frac{x+112}{7}$

⇒ $7x = 3(x+112)$

⇒ $7x=3x+336$

⇒ $7x-3x=336$

⇒ $4x=336$

⇒ $x=\frac{336}{4}$

⇒ $x=84$

Therefore, the number is 84.

Checking:

One-third of the number = $\frac{1}{3} \times 84 = 28$

On-seventh of the number = $\frac{1}{7} \times 84 = 12$

We can write as: $28=12+16$

Therefore, one-third of the number exceeds one-seventh of the number by 16.

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