A number is divided into two parts in such a way that 80%

A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is

First part = ₹ x and second part = ₹ y.
According to question,

	x × 80	=	y × 60	+ 3
	100		100

⇒	4x	=	3y	+ 3
	5		5

⇒ 4x – 3y = 15 ....................(i)
Again,

	4y	=	9x	+ 6
	5		10

⇒ 8y = 9x + 60
⇒ 8y – 9x = 60 ...............(ii)
By equation (i) × 8 + (ii) × 3,

	32x – 24y = 120 24y – 27x = 180
	5x = 300 ⇒ x = 60

From equation (i)
4 × 60– 3y = 15
⇒ 3y = 240 – 15 = 225

⇒ y =	225	= 75
	3

∴ x + y = 60 + 75 = 135