Given:

• A and B received money in a certain ratio


• B and C received money in the same ratio


• A gets Rs.1,60,000


• C gets Rs.2,50,000

To find: The amount received by B





Let the ratio of A and B be x:y.
Then, we can write:

A's share = Rs.1,60,000 = (x/(x+y)) * Total amount

B's share = Rs. ?
We don't know the value of y yet, so let's keep it as it is.



B and C received money in the same ratio.
Let the ratio of B and C be p:q.
Then, we can write:

B's share = (p/(p+q)) * Total amount
C's share = Rs.2,50,000 = (q/(p+q)) * Total amount



We know that A's share is Rs.1,60,000, and C's share is Rs.2,50,000. Let's substitute these values in the equations from Step 1 and Step 2 and equate B's shares.

(x/(x+y)) * Total amount = (p/(p+q)) * Total amount
Cancel out the Total amount from both sides.

(x/(x+y)) = (p/(p+q))
Cross-multiply the above equation.

xp + xq = px + py
Simplify the above equation.

xq = py
Divide both sides by y.

x/y = p/q



We know that A's share is Rs.1,60,000, and B's share is (x/(x+y)) * Total amount.
Substituting x/y = p/q in the above equation, we get:

B's share = (p/(p+q)) * Total amount = [(y/(x+y)) * (p/q)] * Total amount
Let's substitute the values of A's and C's shares.

160000 = (x/(x+y)) * Total amount
250000 = (q/(p+q)) * Total amount

We can eliminate Total amount by dividing the second equation by the first.

250000/160000 = (q/(p+q)) / (x/(x+y))
Simplify the above equation.

25/16 = q/(p+q) * y/x
q/p = (25/16) * (x/y) - 1
q/p = (25/16) * (1/y) - (1/x)

We know that q/p is the same as y/x (from Step 3).
Substituting this value in the above equation, we get:

y/x = (25/16) * (1/y) - (1/x)

Let's assume a value for x, say x = 10. Then, we can calculate y.

Given:- A:B::B:C
B^2= AC
B^2= 1,60,000 × 2,50,000
B = √(1,60, 000 × 2,50,000)
B = 2,00,000
The amount received by B = ₹2,00,000