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

Answer:

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

Step-by-step 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 = $\dfrac{\text{new value - original value}}{{\text{original value}}}\times 100$

Substitute the values, we get,

Changed Percentage = $\frac{1.02xy-xy}{xy}\times 100$

Changed Percentage = $\frac{0.02xy}{xy}\times 100$

Changed Percentage = $0.02\times 100$

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%.