Question

The strength of a school increased
by 20% in one decreased by 20% in
the next year. Is final strength greather
or less than the orignal one, and by
how much percent?​

Answer 1

Answer: The strength is less than 4% of original strength.

Step-by-step explanation: let's say the original strength was 100 if increased by 20% it becomes 120 and then reduced by 20% it becomes 96 i.e. 4% less than the original.

Say it was 150-200 if increased then becomes 180-240 then decreased becomes 144-192 which is 4% less of original (150-200)

Answer 2

Answer :

Strength decreases by 4%

Explanation :

Given that :

The strength of a school increased  by 20%.

Now,

Let the original strength be "y"

Increased :

$\implies\ \sf \dfrac{20}{100} \times y\\\\\implies \sf \dfrac{y}{5}$

Strength after increasing :

$\implies \sf y + \dfrac{y}{5}\\\\\implies \sf \dfrac{(5y+y)}{5}\\\\\implies \sf \dfrac{6y}{5}$

Next year decrease in strength = 20%

Decreased :

$\implies \sf \dfrac{20}{100} \times \dfrac{6y}{5}\\\\\\\implies \sf \dfrac{6y}{25}$

Strength after decreasing :

$\implies \sf \dfrac{6y}{5} - \dfrac{6y}{25}\\\\\implies \sf \dfrac{(30y-6y)}{25}\\\\\implies \sf \dfrac{24y}{25}$

Hence, Final is decreased.

Amount decreased :

$\implies \sf y - \dfrac{24y}{25}\\\\\implies \sf \dfrac{(25y-24y)}{25}\\\\\implies \sf \dfrac {y}{25}$

Percent decreased :

$\implies \sf ( y/25\div y ) \times 100\%\\\\\implies \sf y\25 \times 1/ y \times100\\\\\implies \sf 4\%$

Therefore,

Strength decreases by 4%