Due to increase of 32% in the price of pulse, a person reduces his consumption in such a way that his expenditure increases only by 10%. If he consumes 150kg of pulse after the price has increased then how much pulse was consumed by him initially?

Options

A. 180kg
B. 175kg
C. 190kg
D. 200kg

Answer

To find out how much pulse the person consumed initially, we can follow these steps:

### Step 1: Define the initial price of pulse
Let the initial price of pulse be \( X \) rupees per kg.

### Step 2: Calculate the increased price of pulse
The price of pulse increases by 32%. Therefore, the new price after the increase is:
\[ \text{Increased Price} = X + 0.32X = 1.32X \text{ rupees per kg} \]

### Step 3: Determine the expenditure after the price increase
After the price increase, the person consumes 150 kg of pulse. The expenditure after the price increase can be calculated as:
\[ \text{Expenditure after increase} = \text{Quantity} \times \text{Increased Price} = 150 \times 1.32X = 198X \text{ rupees} \]

### Step 4: Calculate the initial expenditure
We know that the expenditure has increased by 10%. Therefore, if the initial expenditure was \( E \), then:
\[ \text{Expenditure after increase} = E + 0.10E = 1.10E \]
Setting this equal to the expenditure after the price increase, we have:
\[ 1.10E = 198X \]

### Step 5: Solve for the initial expenditure \( E \)
Rearranging the equation gives:
\[ E = \frac{198X}{1.10} \]
Calculating this gives:
\[ E = \frac{198X \times 100}{110} = \frac{1980X}{110} = 180X \text{ rupees} \]

### Step 6: Determine the initial quantity of pulse consumed
The initial expenditure \( E \) can also be expressed in terms of the initial price and quantity:
\[ E = \text{Initial Quantity} \times \text{Initial Price} = Q \times X \]
Setting this equal to our earlier expression for \( E \):
\[ Q \times X = 180X \]
Dividing both sides by \( X \) (assuming \( X \neq 0 \)):
\[ Q = 180 \text{ kg} \]

### Conclusion
The initial quantity of pulse consumed by the person was **180 kg**.

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