Question

By what percent will the product of two numbers change, if the first number increases by 70%, while the second number decreases by 40%.

Answer 1

The product of two numbers changes by 2% when the first number increases by 70%, while the second number decreases by 40%.

Explanation:

Let first number be x and second number be y .

Then product of x and y = xy ......(1)

Given the first number increases by 70%, while the second number decreases by 40% this means,

x is increased by 70% that is

increased value of x = x + 0.7(x) = 1.7 x

Similarly y is decreases by 40% that is

decreased value of y = y - 0.4(y) = 0.6y

New product will be = (increased value of x )( decreased value of y)

= (1.7x)(0.6y)

=1.02xy

Changed Percentage =
`\frac{\text{new value - original value}}{{\text{original value}}}* 100`

Substitute the values, we get,

Changed Percentage =
`(1.02xy-xy)/(xy)* 100`

Changed Percentage =
`(0.02xy)/(xy)* 100`

Changed Percentage =
`0.02* 100`

Changed Percentage =
`2\%`

Thus, the product of two numbers changes by 2% when the first number increases by 70%, while the second number decreases by 40%.