(b) Let the savings of X, Y and Z be ₹ x, ₹ y and ₹ z, respectively.
| ‌Income | x | y | z | =5:7:9 |
| Expenditure | x | y | z | =6:7:12 |
Given, X saves 30% of his income,
∵ Income - Expenditure = Savings
∴ 5x - 6y =
of 5x
⇒ 5x - 6y =
x
⇒ 5x -
x = 6y
⇒
= 6y
⇒
x = 6y
⇒ x =
y=y .........(i)
∴ Savings of X =
×y=y For the person Y, 7x - 7y = Savings
On putting the value of x from Eq. (i), we get
Savings = 7
×y - 7y = 12y - 7y = 5y
Similarly, for person Z Savings = 9x - 12y
On putting savings value of x from Eq. (i), we get
Savings = 9
×y - 12y
=
=y∴ Ratio of their savings = X : Y : Z
=
y:5y:y = 18y : 35y : 24y = 18 : 35 : 24