Question

A four meter elastic band is increased 10%. find its new length.

Answer 1

Final answer: New length of an elastic band = 4.4 $m$

Given that: We are given length of a 4 $m$ elastic band is increased 10%.

To find: We have to find new length of an elastic band.

Explanation:

• Let "$p$" be the initial value of any quantity. The value of quantity is increased or decreased by "$n$%" of its initial value, then the increased or decreased value is given by, $\frac{p*n}{100}=\frac{pn}{100}$

Final value of the quantity =  $p$ ± $\frac{pn}{100}$

The value of quantity is increased. Final value of the quantity $=p+\frac{pn}{100}$

The value of quantity is decreased. Final value of the quantity $=p-\frac{pn}{100}$

Here we apply this rule.

• The initial length of an elastic band = 4 $m$

• Length of an elastic band is increased by 10% of its initial length.

$Increased length of an elastic band= \frac{Initial length of an elastic band *10}{100}$

                                                $=\frac{4*10}{100} =\frac{4}{10} =0.4$ $m$

• So,

$Final length of an elastic band = Initial length + Increased length$

                                              $= 4 + 0.4 = 4.4$ $m$

• Hence, new length of an elastic band = 4.4 $m$

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Answer 2

The new length is 4.4 meters.

• A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolise it. There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
• We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
• The original number is subtracted from the new number, divided by the original number, then multiplied by 100 to get the % increase.

Here, according to the given information, we are given that,

A four meter elastic band is increased 10%.

When the elastic band is 100 meters, the band is increased to a length of 110 meters.

When the elastic band is 1 meter, the band is increased to a length of $\frac{110}{100}$ meters.

When the elastic band is 4 meters, the band is increased to a length of $\frac{11}{10}.4 =4.4$ meters.

Hence, the new length is 4.4 meters.

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