Question

The number of illiterate people in a country decreased from 150 lakhs to 100 lakhs in 10 years. Find the decrease in percentage.

Answer 1

Hint: Assume the number of illiterate people in the country 10 years ago as ${{x}_{1}}$ and the number of illiterate people in the country at present as ${{x}_{2}}$. Find the fractional decrease in the number of illiterate people by using the formula $\dfrac{\left( {{x}_{1}}-{{x}_{2}} \right)}{{{x}_{1}}}$. Multiply the obtained fractional value with 100 to get the percentage decrease.

Complete step by step answer:
Here we have been given that the number of illiterate people in the country decreases from 150 lakhs to 100 lakhs in 10 years. We are asked to find the percentage decrease in the number.
Now, the population of illiterate people 10 years ago $={{x}_{1}}$ = 150 lakhs
The population of illiterate people at present $={{x}_{2}}$ = 100 lakhs
$\Rightarrow $ Decrease in the number of illiterate people $=\left( {{x}_{1}}-{{x}_{2}} \right)$ = (150 – 100) lakhs
$\Rightarrow $ $\left( {{x}_{1}}-{{x}_{2}} \right)$ = 50 lakhs
The fractional decrease in the population of illiterate people will be given as the ratio of decrease to the original number of illiterate people, so we get,
$\Rightarrow $ Fractional decrease = $\dfrac{\left( {{x}_{1}}-{{x}_{2}} \right)}{{{x}_{1}}}$
$\Rightarrow $ Fractional decrease = $\dfrac{50}{150}$
$\Rightarrow $ Fractional decrease = $\dfrac{1}{3}$
Now, the percentage decrease will be equal to 100 multiplied with the fractional decrease, so we get,
$\Rightarrow $ Percentage decrease = $\dfrac{1}{3}\times 100$
$\therefore $ Percentage decrease = $33.33$
Hence, the percentage decrease in the number of illiterate people is 33.33 %.

Note: Always remember that the percentage increase or decrease is calculated upon the initial number and not the final number. This is the reason that we always take the initial number in the denominator of the fractional increase or decrease. Note that for the increase in the number we subtract the initial number from the final number and find the percentage increase as $\dfrac{\left( {{x}_{2}}-{{x}_{1}} \right)}{{{x}_{1}}}\times 100$.