A person of weight 70 kg wants to loose 7 kg by going up and dwon 12 m stairs.Assume he burns twice as much fat while going up than going down.If 1 kg of fat is burnt on expending 9000 k-cal.How many times must he go up and down to reduce his 7 kg weight?
`(Take g=10 ms^(-2))`

Options

A. `18xx10^(3)`times
B. `24xx10^(3)`times
C. `30xx10^(3)`times
D. `21xx10^(3)`times

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total energy required to lose 7 kg of fat.
1 kg of fat is burnt by expending 9000 k-cal. Therefore, to lose 7 kg, the energy required is:
\[ \text{Energy required} = 7 \, \text{kg} \times 9000 \, \text{k-cal/kg} = 63000 \, \text{k-cal} \]

### Step 2: Convert the energy required from k-cal to calories.
Since 1 k-cal = 1000 calories, we have:
\[ 63000 \, \text{k-cal} = 63000 \times 1000 \, \text{calories} = 63000000 \, \text{calories} \]

### Step 3: Calculate the energy expended in one round of going up and down the stairs.
The energy expended while going up is given by the formula \(mgh\), and while coming down it is \(\frac{1}{2}mgh\). Therefore, the total energy expended in one round (up and down) is:
\[ \text{Energy for one round} = mgh + \frac{1}{2}mgh = \frac{3}{2}mgh \]
Where:
- \(m = 70 \, \text{kg}\) (weight of the person)
- \(g = 10 \, \text{m/s}^2\) (acceleration due to gravity)
- \(h = 12 \, \text{m}\) (height of the stairs)

Calculating this gives:
\[ \text{Energy for one round} = \frac{3}{2} \times 70 \, \text{kg} \times 10 \, \text{m/s}^2 \times 12 \, \text{m} = \frac{3}{2} \times 8400 \, \text{J} = 12600 \, \text{J} \]

### Step 4: Convert the energy expended in one round from joules to calories.
Using the conversion \(1 \, \text{cal} = 4.2 \, \text{J}\):
\[ \text{Energy for one round in calories} = \frac{12600 \, \text{J}}{4.2 \, \text{J/cal}} \approx 3000 \, \text{cal} \]

### Step 5: Calculate the number of rounds required to lose 7 kg of fat.
To find the number of rounds needed to burn 63000000 calories:
\[ \text{Number of rounds} = \frac{\text{Total energy required}}{\text{Energy per round}} = \frac{63000000 \, \text{cal}}{3000 \, \text{cal}} = 21000 \]

### Final Answer:
The person must go up and down the stairs **21,000 times** to lose 7 kg of weight.

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