Question

Given that X=ab ,find the percentage increase in X when both a and b increases by 10%.

Answer 1

Answer:

The percentage increase in X is 21%.

Step-by-step explanation:

Given that X=ab ,find the percentage increase in X when both a and b increases by 10%.

Given: X=ab, a is increased by 10%, b is increased by 10%

Asked: The percentage increase in X

Solutions:

Change 10% into decimal and that is 0.10 or 0.1

If a is increased by 10% or 0.1, then it will become,

a + 0.1a

= 1a + 0.1a     It is understood that a has a numerical coefficient of 1.

= 1.1a

If b is increased by 10% or 0.1, then it will become,

b +0.1b

= 1b + 0.1b     It is understood that b has a numerical coefficient of 1.

= 1.1b

Using the given X = ab, when both a and b is increased by 10% or 0.1, then

X = (1.1a) (1.1b)

=1.21ab

In the given X = ab, ab as a numerical coefficient of 1. Thus,

1.21ab - ab

= 1.21ab - 1ab             It is understood that ab has a numerical coefficient of 1.

= 0.21                         Change into percent by moving the decimal point to    the right (two decimal places) and add the percent sign.

= 21% is the percentage increase in X when both a and b increase by 10%