Divide ₹1100 among A, B, and C so that A shall receive [tex]\frac{3}{7}[/tex] of what B and C together receive and B may receive [tex]\frac{2}{9}[/tex] of what A and C receive.
Answer (1)
To solve this problem, we need to understand and set up equations based on the given conditions.
Let's denote the amounts received by A, B, and C as a , b , and c respectively.
The total amount to be divided is 1100 , so we have:
a + b + c = 1100
According to the problem, A receives 7 3 of what B and C together receive, i.e.,
a = 7 3 ( b + c )
Similarly, B receives 9 2 of what A and C together receive, i.e.,
b = 9 2 ( a + c )
Now, let's solve these equations step by step.
Step 1: Express a in terms of b and c
From the equation: a = 7 3 ( b + c )
Step 2: Express b in terms of a and c
With the equation: b = 9 2 ( a + c )
Step 3: Use the total amount equation
Substitute a and b from the above steps into the equation:
a + b + c = 1100
Substitute a = 7 3 ( b + c ) and b = 9 2 ( a + c ) into the total equation to express all terms in terms of one variable, say c .
To do this:
Substitute a = 7 3 ( b + c ) into the equation for b :
b = 9 2 ( 7 3 ( b + c ) + c )
Simplify and solve for b and c :
b = 9 2 ( 7 3 b + 7 3 c + c )
Solve for b in terms of c .
After solving, you will get specific values for b and c . Substitute these back to find a .
Finally, verifying all values should sum to \1 100 and satisfy the original conditions.
This method will give you the amounts each person receives: A, B, and C.
