# There are three articles A, B and C. The price of A increased by 25%. The price of B and C decreased by 25% and 10% respectively. The cost price of A

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There are three articles A, B and C. The price of A increased by 25%. The price of B and C decreased by 25% and 10% respectively. The cost price of A is equal to the selling price of B. The ratio of cost price of C to the selling price of A is 4 : 3. The total cost price of all the three articles is 144. Find the selling price of C.

1. 48
2. 54
3. 50
4. 44

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Correct Answer - Option 2 : 54

Given:

There are three articles A, B and C.

The price of A increased by 25%.

The price of B and C decreased by 25% and 10% respectively.

The cost price of A is equal to the selling price of B.

The ratio of cost price of C to the selling price of A is 4: 3.

The total cost price of all the three articles is 144.

Formula used:

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

Profit percentage = (Profit /Cost Price) x 100

Loss percentage = (Loss / Cost price) x 100

Calculation:

CP of A = x

SP of B = x

CP of C : SP of A = 4 : 3

Let, CP of C = 4y

SP of A = 3y

CP of B = 144 – x – 4y

SP of A = 1.25 × x = 1.25x

1.25x = 3y

⇒ x = 3y/1.25      ---(1)

SP of B = x = 0.75 × (144 – x – 4y)

⇒ x = 0.75 × (144 – x – 4y)

⇒ x = 108 - 0.75x - 3y

⇒ 1.75x = 108 - 3y

⇒ 1.75 × 3y/1.25 = 108 - 3y

⇒ 4.2y + 3y = 108

⇒ y = 15

From (1),

x = (3 × 15)/1.25 = 36

SP of C = 4y × (0.9) = 3.6y = 3.6 × 15 = 54

Solving (1) and (2), we get

SP of C = 54

∴ SP of C is Rs. 54