a sum of money is to be divided among A,B and C in the ratio 2:3:5. the largest share amount to $1200.
calculate: the total sum of money to be shared
ii} A's share
iii} the percentage of the total amount that B receives
2:3:5 = 480:720:1200
(a) 480+720+1200
(b) 480
(c) 720/(a)
800
To calculate the total sum of money to be shared, we need to find the common ratio. Since the ratio of shares is given as 2:3:5, the common ratio is the sum of the ratio parts: 2+3+5 = 10.
i) Total sum of money to be shared: Multiplying the largest share amount by the common ratio:
Total sum = Largest share / (largest share ratio part / common ratio)
Total sum = $1200 / (5 / 10) = $1200 / 0.5 = $2400.
ii) A's Share: Calculating A's share based on the given ratio:
A's share = Total sum × (A's ratio part / common ratio)
A's share = $2400 × (2 / 10) = $480.
iii) Percentage of the total amount that B receives: Calculating B's share as a percentage of the total sum:
B's share = Total sum × (B's ratio part / common ratio)
B's share = $2400 × (3 / 10) = $720.
Percentage of B's share = (B's share / Total sum) × 100
Percentage of B's share = ($720 / $2400) × 100 = 30%.
To find the total sum of money to be shared, we need to determine the value of the smallest part in the ratio.
Let’s assume the smallest part of the ratio is "x".
Then the ratio becomes 2x:3x:5x.
We know that the largest share (C's share) amounts to $1200.
According to the given ratio, this represents 5x.
So, we can set up the equation:
5x = 1200
Now, solve for x:
x = 1200/5
x = 240
Now, we can find the other parts of the ratio:
A's share = 2x = 2 * 240 = $480
The total sum of money to be shared is the sum of all the shares:
Total sum = A's share + B's share + C's share
Total sum = $480 + 3x + $1200
To calculate B's share, we can substitute x = 240 into the ratio:
B's share = 3 * x = 3 * 240 = $720
The percentage of the total amount that B receives can be calculated as:
Percentage for B = (B's share / Total sum) * 100
Percentage for B = ($720 / (480 + 720 + 1200)) * 100
Now, calculate the percentage for B.