Question

Raja walked 36 km on Monday and on Tuesday he walked $10\% $ more. How much distance did he cover on both days put together ?

Answer 1

Hint: Percent – Percent means hundredths or per hundred and is written with the symbol $\% $. Percent is a ratio where we compare numbers to 100 which means that $1\% $ is $\dfrac{1}{{100}}$.
Like, $25\% $ can be written as $\dfrac{{25}}{{100}} = \dfrac{1}{4}$
Or,
$20\% $ of $600 = \dfrac{{20}}{{100}} \times 600 = 120$

Complete step-by-step answer:
Percent changes applied sequentially do not add up in the usual way. For example, if the 10% increase in price considered earlier (on the 200 RS item, raising its price to 220 RS) is followed by a 10% decrease in the price (a decrease of 22 RS), then the final price will be 198 RS—not the original price of 200 RS. The reason for this apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different quantities (200 RS and 220 RS, respectively), and thus do not "cancel out".
Total distance covered on Monday $ = $ 36 km
Distance covered on Tuesday $ = 36 + 10\% $ of 36
So, distance covered on Tuesday $ = 36 + \dfrac{{10}}{{100}} \times 36 = (36 + 3.6)km$
$ = 39.6km$
Therefore, total distance travelled by him in both the days,
$ = (36 + 39.6)km$
$ = 75.6km$

Note: In above question distance covered by Raja on Tuesday is $10\% $ more than distance covered on Monday.
We can also solve this by following formulas also.
Increase N by $S\% = N\left( {1 + \dfrac{S}{{100}}} \right)$
Here we are increasing 36 by $10\% $ so $N = 36$ and $S = 10$
Distance covered on Tuesday $ = 36\left( {1 + \dfrac{{10}}{{100}}} \right)km$
$ = 36(1 + 0.1)km$
$ = (36 \times 1.1)km$
$ = 39.6km$