Question

There are 12 pieces of five, ten and twenty rupee currencies whose total value is 105
When first 2 sorts are interchanged in their numbers its value will be increased by
20. Find the number of currencies in each sort.​

Answer 1

Answer:

• ₹5 notes = 7
• ₹10 notes = 3
• ₹20 = 2

Explanation:

Let,

• The currencies be x, y and z respectively
• ₹5 notes be 'x' = 5x
• ₹10 notes be 'y' = 10y
• ₹20 notes be 'z' = 20z

There are 12 pieces,

• x + y + z = 12 -------- (1)

Total value of 5,10 and 20 currencies are 105,

• 5x + 10y + 20z = 105 --------- (2)

2 sorts changed, it's value is increased by 20,

⟼ 5y + 10x + 20z = 105 + 20

⟼ 5y + 10x + 20z = 125 ---------- (3)

Solving (2) & (3),

5x + 10y + 20z = 105 (-)

10x + 5y + 20z = 125

________________

-5x + 5y = -20 ------------(4)

________________

Solving (1) & (2),

To make 'z' value same in both (1) & (2), we will multiply (1) × 20,

20x + 20y + 20z = 140 (-)

5x + 10y + 20z = 105

_________________

15x + 10y = 135 ----------- (5)

_________________

Solving (4) & (5),

To make 'y' value same in both (4) & (5), we have to multiply (4) × 2,

-10x + 10y = -40 (-)

15x + 10y = 135

____________

-25x = -175

____________

⟼ x = -175 / 25

⟼ x = 7

Substituting 'x' value in (4),

⟼ -5x + 5y = -20

⟼ -5(7) + 5y = -20

⟼ -35 + 5y = -20

⟼ 5y = -20 + 35

⟼ 5y = 15

⟼ y = 15 / 5

⟼ y = 3

Substituting 'x' and 'y' in (1),

⟼ x + y + z = 12

⟼ 7 + 3 + z = 12

⟼ 10 + z = 12

⟼ z = 12 - 10

⟼ z = 2

• ∴ ₹5 notes = 7, ₹10 notes = 3 and ₹20 = 2