Understanding the Wheat Production Data

The problem provides a table showing the percentage distribution of wheat production across seven countries and the distribution within each country based on two methods: Scientific and Conventional. The total wheat production across all seven countries is given as 50 lakh tonnes.

We need to find the ratio of the wheat production by the Conventional Method in Pakistan to the wheat production by the Scientific Method in Japan.

Calculating Production Amounts

To find the ratio, we first need to calculate the actual production quantities for the specified categories.

Step 1: Calculate Total Production in Pakistan

According to the table, Pakistan accounts for 9% of the total wheat production (50 lakh tonnes).

Total production in Pakistan = 9% of 50 lakh tonnes

Total production in Pakistan = $\frac{9}{100} \times 50$ lakh tonnes

Step 2: Calculate Conventional Production in Pakistan

Within Pakistan, 34% of the wheat is produced using the Conventional Method.

Conventional production in Pakistan = 34% of (Total production in Pakistan)

Conventional production in Pakistan = $\frac{34}{100} \times \left(\frac{9}{100} \times 50\right)$ lakh tonnes

Step 3: Calculate Total Production in Japan

According to the table, Japan accounts for 20% of the total wheat production (50 lakh tonnes).

Total production in Japan = 20% of 50 lakh tonnes

Total production in Japan = $\frac{20}{100} \times 50$ lakh tonnes

Step 4: Calculate Scientific Production in Japan

Within Japan, 78% of the wheat is produced using the Scientific Method.

Scientific production in Japan = 78% of (Total production in Japan)

Scientific production in Japan = $\frac{78}{100} \times \left(\frac{20}{100} \times 50\right)$ lakh tonnes

Finding the Ratio

Now, we need to find the ratio of Conventional production in Pakistan to Scientific production in Japan.

Ratio = (Conventional production in Pakistan) : (Scientific production in Japan)

Ratio = $\left(\frac{34}{100} \times \frac{9}{100} \times 50\right) : \left(\frac{78}{100} \times \frac{20}{100} \times 50\right)$

We can simplify the ratio by canceling out the common factors on both sides. Both expressions have $\frac{1}{100} \times 50$ as a factor.

Ratio = $\left(\frac{34}{100} \times 9\right) : \left(\frac{78}{100} \times 20\right)$

Now, multiply the numbers:

Conventional production (relative) in Pakistan = $\frac{34 \times 9}{100} = \frac{306}{100}$

Scientific production (relative) in Japan = $\frac{78 \times 20}{100} = \frac{1560}{100}$

So the ratio is $\frac{306}{100} : \frac{1560}{100}$. We can multiply both sides by 100 to simplify:

Ratio = $306 : 1560$

Now, simplify the ratio $306 : 1560$ by finding the greatest common divisor (GCD).

Both numbers are even, so divide by 2:

$306 \div 2 = 153$

$1560 \div 2 = 780$

The ratio is $153 : 780$.

Check for other common factors. The sum of digits of 153 is $1+5+3=9$, which is divisible by 3 and 9. The sum of digits of 780 is $7+8+0=15$, which is divisible by 3. So, both numbers are divisible by 3.

$153 \div 3 = 51$

$780 \div 3 = 260$

The ratio is $51 : 260$.

Now check if 51 and 260 have any common factors. Factors of 51 are 1, 3, 17, 51. 260 is not divisible by 3 or 17 or 51. So, the ratio $51 : 260$ is in its simplest form.

Therefore, the ratio of production of wheat by Conventional Method in Pakistan to that by the Scientific Method in Japan is $51 : 260$.

Revision Table: Wheat Production Data Summary

Additional Information on Data Interpretation Ratios

When calculating ratios from percentage data like this, it is important to understand what each percentage represents.

• The first column of percentages shows the proportion of the total production (50 lakh tonnes) that comes from each country.
• The next two columns show the proportion of that country's production that uses either the Scientific or Conventional method.

To find the amount produced by a specific method in a specific country, you multiply the total production by the country's overall percentage, and then multiply that result by the percentage for the specific method within that country. However, as shown in the steps above, when calculating a ratio between two such values, the 'total production' factor often cancels out, simplifying the calculation to just the product of the relevant percentages for each part of the ratio, adjusted for the country's overall share.