Question

A number is increased by 40% then decreased by 30% find the net increase or decrease percent

Answer 1

Step-by-step explanation:

(there is a minor error in your question, the decrease is not 30%, it is 40%)

Let us assume that the number be 100.

At first we have to increase the number by 40%.

Then we have to decrease 40% again.so, firstly, after increase the term by 40% , we have the number be

100 + 100*40/100

= 100 + 40= 140

Again, we have to decrease the number by 40%.

So, the number becomes

140 - 140*40/100= 140 - 56= 84

So, we have seen that the number decrease.

Now we have to calculate the percentage of the number has decreased.

Assumed number = 100

Present number = 84

So, decrease percentage = 16 % (ans.)

Answer 2

Answer:

The correct answer is 1%.

Step-by-step explanation:

Step 1

Let the number be $x.$

Increased percentage $=40 \%$

then the number will be

$x+\frac{40 x}{100}=\frac{140 x}{100}$

Step 2

Decreased percentage $=30 \%$

$\frac{140 x}{100}-\left(\frac{140 x}{100} \times \frac{30}{100}\right)$

Apply rule: $\quad-(a)=-a$

$&-\left(\frac{140 x}{100} \times \frac{30}{100}\right)=-\frac{140 x}{100} \times \frac{30}{100}$

$&=\frac{140 x}{100}-\frac{140 x}{100} \times \frac{30}{100}\end{aligned}$

Factor out the common term

$\frac{140 x}{100}: \frac{140 x}{100}\left(1-\frac{30}{100}\right)$

$&=\frac{140 \mathrm{0} x}{100}\left(1-\frac{30}{100})\right.$

$&1-\frac{30}{100}=\frac{7}{10}$

$&=\frac{140 \mathrm{0} x}{100} \times \frac{7}{10}\end{aligned}$

Cancel$\frac{140 x}{100}: \frac{7 x}{5}$

$=\frac{7 x}{5} \times \frac{7}{10}$

Step 3

Apply the fraction rule:

$\quad \frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$

$=\frac{7 x \times 7}{5 \times 10}$

Multiply the numbers: $7 \times 7=49$

$=\frac{49 x}{5 \times 10}$

Multiply the numbers: $5 \times 10=50$

$=\frac{49 x}{50}$

Step 4

Decreased percentage

= $x-\left(\frac{49 x}{50}\right)$

Apply rule: $\quad-(a)=-a$

$&-\left(\frac{49 x}{50}\right)=-\frac{49 x}{50}$

$&=x-\frac{49 x}{50}\end{aligned}$

Step 5

Apply the fraction rule: $\quad a-\frac{b}{c}=\frac{a c-b}{c}$

$=\frac{x \cdot 50-49 x}{50}$

Add similar elements: $x-50-49 x=x$

$=\frac{x}{50}$

Therefore, the correct answer is 1%.

#SPJ3