Shveta distributed y kg rice and x kg wheat to each family which comes under BPL of her society where
x and y are the natural numbers which satisfy 8x + 3y = 96 and x
then find the total quantity of rice and wheat respectively distributed by Shveta.

To solve the problem of how much rice and wheat Shveta distributed, we first need to analyze the equation given: 8x + 3y = 96. Here, x represents the kilograms of wheat and y represents the kilograms of rice distributed to each family. Our goal is to find the total quantity of rice and wheat distributed, given that x and y are natural numbers.

Breaking Down the Equation

The equation 8x + 3y = 96 can be understood as a linear equation in two variables. To find suitable values for x and y, we can express y in terms of x:

3y = 96 - 8x

y = (96 - 8x) / 3

Finding Natural Number Solutions

Since y must be a natural number, the expression (96 - 8x) must be divisible by 3. Let's analyze this condition:

• First, we can check the value of 96 modulo 3:
• 96 mod 3 = 0 (since 96 is divisible by 3).
• Next, we check the term 8x mod 3:
• 8 mod 3 = 2, so 8x mod 3 = 2x mod 3.

For (96 - 8x) to be divisible by 3, we need:

0 - 2x ≡ 0 (mod 3)

This implies that 2x must also be congruent to 0 modulo 3. Therefore, x must be a multiple of 3.

Finding Possible Values for x

Now, let's find the possible values for x that are natural numbers and satisfy the equation:

• Let x = 3:

y = (96 - 8*3) / 3 = (96 - 24) / 3 = 72 / 3 = 24

• Let x = 6:

y = (96 - 8*6) / 3 = (96 - 48) / 3 = 48 / 3 = 16

• Let x = 9:

y = (96 - 8*9) / 3 = (96 - 72) / 3 = 24 / 3 = 8

• Let x = 12:

y = (96 - 8*12) / 3 = (96 - 96) / 3 = 0 / 3 = 0 (not a natural number)

Thus, the valid pairs (x, y) that satisfy the equation are:

• (3, 24)
• (6, 16)
• (9, 8)

Calculating Total Quantities Distributed

Now, let's calculate the total quantities of rice and wheat distributed for each pair:

• For (3, 24):

Total wheat = 3 kg, Total rice = 24 kg

• For (6, 16):

Total wheat = 6 kg, Total rice = 16 kg

• For (9, 8):

Total wheat = 9 kg, Total rice = 8 kg

Summary of Distribution

In summary, Shveta distributed the following quantities:

• 3 kg of wheat and 24 kg of rice to each family in the first case.
• 6 kg of wheat and 16 kg of rice in the second case.
• 9 kg of wheat and 8 kg of rice in the third case.

To find the total quantity distributed, you would multiply the amounts by the number of families receiving the distribution. If you know how many families are involved, you can easily calculate the total quantities of rice and wheat distributed by Shveta.