Problem 13: 60% of 3/8 of a number is 180. find the number?
Problem 13: 60% of 3/8 of a number is 180. find the number?
Solution:
In this problem, we just start with a supposition of the number and finish with the percentage calculation.
That is we suppose:
\[ The Number =x \]
\[ \frac{3}{8} OfThe Number= \frac{3}{8}x \]
or
\[ =\frac{3x}{8} \]
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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eye test for you!