Question

By what percent will the product of two numbers increase if one of them is increased by 30% and the other is increased by 20%?

Answer 1

We have for example 2 numbers, a and b, and their product, number c.
So,
c = a * b
If value of a is increased by 30 percent, it means that the new value will be old value plus 30 percent of the value; so new value is:
a1 = a + 30% * a
If we elaborate this equation, we get:
a1 = a + 30/100 * a, i.e.:
a1 = 100/100 * a + 30/100 * a, i.e.:
a1 = (100+30)/100 * a, i.e.:
a1 = 130/100 * a .
Same for other number b:
It its value is increased by 20 percent, it means that the new value will be old value plus 20 percent of the value:
b1 will be the notation for the new value, and b is the old value
b1 = b + 20% * b
b1 = 120% * b
b1 = 120/100 * b
-------------------------------------
When wanting to multiply a1 with b1, we get:
c1 = a1 * b1
c1 = 130/100 * a * 120/100 * b
When reducing fractions, we get:
c1 = 13/10 * a * 12/10 * b
When multiplying free numbers and move the order of a and b, we get:
c1 = (13*12)/(10*10)*a*b
c1 = 156/100 * a * b
-> a * b is c (c = a * b), so:
c1 = 156% * c
c1 = (100 + 56)% * c
Which means that the value of c is increased by 56%.