Rs 770 have been divided among A,B,C in such a way that A receives 2/9 th of what B and C together receive.then A share?
Let's solve this problem step by step:
1. Let's assume that B and C together receive x rupees.
2. According to the given information, A receives 2/9 times (B + C), which can be expressed as (2/9) * x.
3. We know that the total amount of money is Rs 770, so the equation can be written as:
A + B + C = 770.
4. Now, substitute the value of A from step 2 into the equation:
(2/9) * x + B + C = 770.
5. Simplify the equation by multiplying both sides by 9 to get rid of the fraction:
2x + 9B + 9C = 6930.
6. Since we assumed B + C = x, we can rewrite the equation as:
2x + 9(x) = 6930.
7. Combine like terms on the left side of the equation:
2x + 9x = 6930.
11x = 6930.
8. Divide both sides of the equation by 11 to solve for x:
x = 630.
9. Now substitute the value of x back into the equation B + C = x:
B + C = 630.
10. Since B + C = 630, we can divide it equally between B and C to find their individual shares:
B = C = 630/2 = 315.
11. Finally, substitute the value of B and C into the equation A + B + C = 770 to find A's share:
A + 315 + 315 = 770.
A + 630 = 770.
A = 770 - 630.
A = 140.
Therefore, A's share is Rs 140.
To find A's share, we need to first determine the total amount that B and C receive together.
Let's assume that B and C together receive x amount.
According to the given information, A receives 2/9th of what B and C together receive. Therefore, A's share can be calculated as (2/9) * x.
Since the total amount distributed is Rs 770, we can set up the equation:
A's share + B's share + C's share = Total amount
(2/9) * x + x + x = 770
To simplify the equation, we can rewrite (2/9) as (2x/9):
(2x/9) + x + x = 770
Now, we can solve this equation to find the value of x, which represents the amount that B and C together receive.
Multiply each term by 9 to eliminate the fraction:
2x + 9x + 9x = 770 * 9
20x = 6930
Divide both sides by 20:
x = 6930 / 20
x = 346.50
Now that we know x, we can find A's share:
A's share = (2/9) * x
A's share = (2/9) * 346.50
A's share ≈ 76.83
Therefore, A's share is approximately Rs 76.83.
a+b+c = 770
a = 2/9 (b+c) ==> b+c = 9a/2
a + 9a/2 = 770
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