When the price of an item was reduced by 35%, then its sale was increased by x%. If there is an increase of 17% in the receipt of the revenue, then the value of x will be:

Options

A. 84
B. 80
C. 60
D. 75

Answer

To solve the problem, we need to determine the percentage increase in sales (x%) after a 35% reduction in price that results in a 17% increase in revenue.

Let's break this down step by step:

### Step 1: Define the initial conditions
Assume the initial price of the item is 100 rupees, and the initial quantity sold is 100 units.

- Initial Price (P) = 100 rupees
- Initial Quantity Sold (Q) = 100 units
- Initial Revenue (R) = P * Q = 100 * 100 = 10,000 rupees

### Step 2: Calculate the new price after a 35% reduction
The price is reduced by 35%.

- New Price (P') = P - (35% of P)
- New Price (P') = 100 - (0.35 * 100) = 100 - 35 = 65 rupees

### Step 3: Set up the equation for new revenue
Let the new quantity sold after the price reduction be Q'. According to the problem, the revenue increases by 17%.

- New Revenue (R') = R + (17% of R)
- New Revenue (R') = 10,000 + (0.17 * 10,000) = 10,000 + 1,700 = 11,700 rupees

### Step 4: Relate new revenue to new price and new quantity sold
The new revenue can also be expressed as:

- New Revenue (R') = New Price (P') * New Quantity Sold (Q')
- 11,700 = 65 * Q'

### Step 5: Solve for the new quantity sold (Q')
Now we can find Q':

- Q' = 11,700 / 65
- Q' = 180 units (approximately)

### Step 6: Calculate the percentage increase in quantity sold (x%)
Now we can find the percentage increase in quantity sold:

- Increase in quantity sold = Q' - Q = 180 - 100 = 80 units
- Percentage increase (x) = (Increase / Original Quantity) * 100
- Percentage increase (x) = (80 / 100) * 100 = 80%

### Conclusion
The value of x, the percentage increase in sales, is 80%.

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