Problem 13: 60% of 3/8 of a number is 180. find the number?

Career test math Problems 0

Solution:

In this problem, we just start with a supposition of the number and finish with the percentage calculation.

That is we suppose:

\[ The Number =x \]

\[ \frac{3}{8} OfThe Number= \frac{3}{8}x \]

\[ =\frac{3x}{8} \]

As per given statement ;

60 % of the 3/8 of the number is to be calculated by using percentage formula;

\[ 60 Percent Of The (3/8) Of The Given Number= \frac{60}{100}\times (\frac{3x}{8}) \]

which on simplification will look as under;

\[ 60 Percent Of The (3/8) Of The Given Number= (\frac{9x}{40}) \]

But in the statement 60% of the 3/8 of number = 180

so we should have;

\[ \frac{9x}{40}= 180 \]

hence,

\[ \frac{9x}{40}=180 \]

so,

\[ x= \frac{180\times 40}{9}=20 \times 40=800 \]

Check:

We can check this in accordance with the conditions given in the statement now!

\[ \frac{3}{8} Of 800=\frac{3}{8} \times 800=300 \]

And now we calculate 60 percent of 300;

\[ 60Percent Of 300=\frac{60}{100}\times300=180 \]

Hence the proof !

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