Question

An elastic band which is 42cm long , is stretched to 70cm. Find the percentage increase in it's length.

Answer 1

Answer:

66.66%

Step-by-step explanation:

As per the provided information in the given question, we have :

• Original length of elastic band = 42 cm
• New length of elastic band = 70 cm

We are asked to calculate,

• Percentage increase

It is an increase from 42 to 70. We have to apply the formula given below,

$\longmapsto \underline{\underline{\boxed{\rm {\% \; increase = \Bigg ( \dfrac{Amount_{(Increase)}}{Amount_{(Original)}} \times 100 \Bigg ) \; \%}}}}$

Step 1 : Finding the amount of increase in length first.

Let's find out the amount of increase in length first.

$\longmapsto \rm { Amount_{(Increase)} = New \; Length- Original Length}$

Substitute the values.

$\longmapsto \rm { Amount_{(Increase)} = 70 - 42}$

Subtracting 42 from 70.

$\longmapsto \rm { Amount_{(Increase)} = 28}$

Step 2 : Substitute all the values in the formula to calculate the required answer.

$\longmapsto \rm {\% \; increase = \Bigg ( \dfrac{Amount_{(Increase)}}{Amount_{(Original)}} \times 100 \Bigg ) \; \%}$

Substitute the values.

$\longmapsto \rm {\% \; increase = \Bigg ( \dfrac{28}{42} \times 100 \Bigg ) \; \%}$

Multiplying the fraction with 100.

$\longmapsto \rm {\% \; increase = \Bigg ( \dfrac{2800}{42} \Bigg ) \; \%}$

Reducing it to the lowest terms. Dividing the numerator and the denominator with 2.

$\longmapsto \rm {\% \; increase = \Bigg ( \dfrac{1400}{21} \Bigg ) \; \%}$

Reducing it to the lowest terms. Dividing the numerator and the denominator with 7.

$\longmapsto \rm {\% \; increase = \Bigg ( \cancel{\dfrac{200}{3}} \Bigg ) \; \%}$

Dividing 200 by 3.

$\longmapsto \bf {\% \; increase = 66.66 \; \%}$

∴ Percentage increase is 66.66%.