PRACTICE SET 5.2 (Algebra) 9th Standard, Linear Equations in Two Variables

In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is ₹350. The number of 5 rupee notes are less by 10 than twice the number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.

Solution: let the number of 5 rupees notes be X and let the number of 10 rupees notes be y.
∴ The total value of x rupees note = 5 × X rupees
∴ The total value of y rupees note = 10 × y rupees
From first condition ‘the total amount of these note together is 350’
∴ 5x + 10y = 350
Dividing both side by 5, we get
∴ X + 2y = 70 …… (i)
From the second condition,
Number of 5 rupee (x) notes less ( minus ) by 10 than twice (2y) the number of 10 rupee notes.
∴ 2y – X = 10
∴ -x + 2y = 10 ….. (ii)
Adding equation (i) and (ii)
X + 2y = 70 …… (i)
-x + 2y = 10 ….. (ii)
——————————————
4y = 80
y = 80 ÷ 40
∴ y= 2
Substituting y = 20 in equation (i)
X + 2y = 70 …… (i)
X + 2×20 = 70
X + 40 = 70
X = 70 – 40
X = 30
Answer: There are 30 notes of 5 rupee (x) notes, and 20 notes of 10 rupee.

The denominator of a fraction is 1 less than twice its numerator. If 1 is added to the numerator and the denominator respectively, the ratio of the numerator to the denominator is 3:5. Find the fraction.