# The ratio of CP of A and SP of B is 21 : 20. The ratio of CP of B and SP of A is 14 : 15. Total SP of both items is Rs. 100 more than the total CP.

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The ratio of CP of A and SP of B is 21 : 20. The ratio of CP of B and SP of A is 14  : 15. Total SP of both items is Rs. 100 more than the total CP.  On selling B. Loss of Rs. 800 was incurred. Find the gain on selling A.

1. 1000
2. 1200
3. 900
4. 850

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Correct Answer - Option 3 : 900

Given:

The ratio of CP of A and SP of B is 21 : 20.

The ratio of CP of B and SP of A is 14  : 15.

Total SP of both items is Rs. 100 more than the total CP.

On selling B. Loss of Rs. 800 was incurred.

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:

Let the CP of A = 21x

SP of B = 20x

Let CP of B = 14y

SP of A = 15y

15y + 20x = 100 + 21x + 14y

⇒ Y = 100 + x      ----(i)

14y – 20x = 800

⇒ 14(100 + x) – 20x = 800 [From (i)]

⇒ 1400 + 14x - 20x = 800

⇒ - 6x = - 600

⇒ x = 100

From equation (i),

y = 100 + x

⇒ y = 100 + 100

⇒ y = 200

CP of A = Rs. (21 × 100) = Rs. 2100

SP of A = Rs. (15 × 200) = Rs. 3000

Gain on selling A = Rs. (3000 - 2100) = Rs. 900

∴ gain on selling A is Rs. 900