Question

The sum of two numbers is 520. if the bigger number is decreased by 4% and the smaller number incresed by 12%, then the numbers obtained are equal. the smaller number is

Answer 1

Let the bigger number is a and the smaller number is (520 - a)

According to the question,

a×(100−4)100=(520−a)×(100+12100)a×(100−4)100=(520−a)×(100+12100)

96a100=(520−a)11210096a100=(520−a)112100

96a=(520−a)11296a=(520−a)112

13a=364013a=3640

a=280

Answer 2

Let the bigger number be x

The smaller number is (520 - x)

The bigger number is decreased by 4%:

4% of the number = 0.04x

Number after decreased = x - 0.04x = 0.96x

The smaller number is increased by 12%:

increased = 0.12( 520 - x) = 62.4 - 0.12x

Number after increased = (520 - x) + (62.4 - 0.12x) = 582.4 - 1.12x

Solve x:

Given that the two numbers obtained are equal

582.4 - 1.12x = 0.96x

1.12x + 0.96x = 582.4

2.06x = 582.4

x = 280

Find the numbers:

The bigger number = x = 280

The smaller number = 520 - x = 520 - 280 = 240

Answer: The smaller number is 240