Rs. 120 is divided among A, B and C so that A's share is Rs. 20 more than B's and Rs. 20 less than C's. The B's share is

Let's solve the problem step by step.

We are given:
- Total amount to be divided = Rs. 120
- A's share is Rs. 20 more than B's share.
- A's share is Rs. 20 less than C's share.

Let's denote:
- B's share as \( B \)
- A's share as \( A \)
- C's share as \( C \)

From the problem, we have the following relationships:
\[ A = B + 20 \quad \text{(since A's share is Rs. 20 more than B's)} \]
\[ C = A + 20 \quad \text{(since A's share is Rs. 20 less than C's)} \]

We also know:
\[ A + B + C = 120 \]

Substituting the values of \( A \) and \( C \) in terms of \( B \):

\[ (B + 20) + B + (B + 20 + 20) = 120 \]

Simplify the equation:
\[ B + 20 + B + B + 40 = 120 \]
\[ 3B + 60 = 120 \]

Now, solve for \( B \):
\[ 3B = 120 - 60 \]
\[ 3B = 60 \]
\[ B = \frac{60}{3} \]
\[ B = 20 \]

So, B's share is Rs. 20.

Would you like more details or have any questions?

Here are five related questions:
1. If A's share was Rs. 30 more than B's, what would B's share be?
2. If C's share was double that of B's, how would the shares change?
3. What if the total amount was Rs. 180 instead of Rs. 120?
4. How would the shares be distributed if B's share was half of A's?
5. What if A's share was Rs. 10 less than B's share?

**Tip:** When dealing with algebraic word problems, defining variables and translating the problem into equations is key to solving it effectively.

Learn how to solve a division problem involving Rs. 120 among A, B, and C, where A's share is Rs. 20 more than B's. This problem covers key algebraic concepts, including equations and word problems. Suitable for students in Grades 7-9.

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