Question

.
4. The population of a place in a particular year increased by 15%. Next year, it decreased by 15%. Find
net increase or decrease percent in the initial population.​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Initial population be p

${\boxed{\sf\:{Population\;after\;1^{st}\;year}}}$

Increase = 15% of p

= 0.15p

${\boxed{\sf\:{Population}}}$

= p + 0.15p

= 1.15p

${\boxed{\sf\:{Population\;after\;2^{nd}\;year}}}$

${\boxed{\sf\:{Decrease}}}$

= 15% of 1.15p

= 0.15(1.15p)

= 0.1725p

${\boxed{\sf\:{Population}}}$

= 1.15p - 0.1725p

=  0.9775p

${\boxed{\sf\:{Net\;Decrease}}}$

= p - 0.9775p

= 0.0225

${\boxed{\sf\:{Percentage\;Decrease}}}$

$\tt{\rightarrow\dfrac{Decrease}{Original}\times 100}$

$\tt{\rightarrow\dfrac{0.0225p}{p}\times 100}$

= 2.25%

Answer 2

Answer:

${\pink{\green{\sf{\therefore Decrease \%=2.25\%}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about population in a particular year and in next year population increases then in second year population decreases.

• We have to find net increase or decrease percent in the initial population.

$\underline \bold{Given : } \\ \implies First \: year \: Increase = 15 \% \\ \implies Second \: year \: decrease = 15 \% \\ \\ \underline \bold{To \:Find : } \\ \implies Net \: increase \: or \: de crease \% = ?$

• According to given question :

$\bold {Let \: population \: be \: x} \\ \bold{First \: year \: increase} \\ \implies 15 \% \: of \: x \\ \implies \frac{15}{10 0 } \times x \\ \bold{\implies 0.15x }\\ \\ \bold{Increased \: population}\\ \implies x + 0.15x \\ \bold{\implies 1.15x} \\ \\ \bold{Second \: year \: decrease} \\ \implies 15 \% \: of \: 1.15x \\ \implies \frac{15}{100} \times \frac{115x}{100} \\ \implies \frac{1725x}{10000} \\ \implies 0.1725x \\ \\ \bold{Decreased \: population} \\ \implies 1.15x - 0.1725 \\ \bold{\implies 0.9775x} \\ \\ So, \: Decreased \: population \: is \: less \\ than \: initial \: population \\ \\ \bold{Net \: Decrease} \\ \implies (Initial - final)population \\ \implies x - 0.9775x \\ \implies 0.0225x \\ \\ \bold{net \: decrease \%} \\ \implies \frac{0.0225x}{x} \times 100 \\ \implies 0.0225 \times 100 \\ \bold{\implies 2.25 \% } \\ \\ \bold{\therefore Decrease \% = 2.25 \%}$