Question

Divide 500 into two parts such that 50% of one exceeds 70% of the other by 10.

Answer 1

Let the two parts be x and y

Then,
x + y = 500 …………[1]

Also,
50% of x = 70% of y + 10
x/2 = 7y/10 + 10
x/2 - 7y/10 = 10
5x - 7y = 100 ……………[2]

Multiply equation [1] with 7 and add it to equation [2]
7x + 7y + 5x - 7y = 3500 + 100
12x = 3600
x = 300

If x is 300 then y = 200 (∵ from equation [1])

∴ The two parts are 300 and 200