A four digit number LMNP is such that its digits follow M+N=P, L+M+1 = P, and 3(1+N)= P. Find the sum of the two numbers LMNP and PNML. LMNP అనే నాలుగు అంకెల సంఖ్యలోని అంకెలు M+N=P, L+M+1=P, 3(1+N) = P అయ్యేట్లుగా ఉంటే, LMNP మరియు PNML అనే సంఖ్యల మొత్తం కనుక్కోండి.

 A four digit number LMNP is such that its digits follow M+N=P, L+M+1 = P, and 3(1+N)= P. Find the sum of the two numbers LMNP and PNML.

LMNP అనే నాలుగు అంకెల సంఖ్యలోని అంకెలు M+N=P, L+M+1=P, 3(1+N) = P అయ్యేట్లుగా ఉంటే, LMNP మరియు PNML అనే సంఖ్యల మొత్తం కనుక్కోండి.

Let's solve the given clues step-by-step.

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We are given a 4-digit number LMNP, where:

• L, M, N, P are digits (0–9), and L ≠ 0 (since it's a 4-digit number).
• The following conditions are given:

1. M + N = P
2. L + M + 1 = P
3. 3(1 + N) = P

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Step 1: Use Equation (3)

From condition (3):

3(1 + N) = P
⇒ 3 + 3N = P

So,

P = 3 + 3N
We'll substitute this into the other equations.

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Step 2: Use condition (1):

M + N = P
But from above, P = 3 + 3N
So,

M + N = 3 + 3N
⇒ M = 3 + 3N – N = 3 + 2N

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Step 3: Use condition (2):

L + M + 1 = P
Substitute M and P:

L + (3 + 2N) + 1 = 3 + 3N
⇒ L + 4 + 2N = 3 + 3N
⇒ L + 4 = 3 + N
⇒ L = -1 + N

Now we check for valid digit values.

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Try integer values for N (0 to 9), and test whether all digits L, M, N, P are valid digits (0–9), and L ≠ 0.

Try N = 2:

• Then L = -1 + 2 = 1 ✅
• M = 3 + 2×2 = 7 ✅
• P = 3 + 3×2 = 9 ✅

Now LMNP = 1 7 2 9

Let’s verify the three conditions:

1. M + N = 7 + 2 = 9 = P ✅
2. L + M + 1 = 1 + 7 + 1 = 9 = P ✅
3. 3(1 + N) = 3(3) = 9 = P ✅

Perfect.

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Step 4: Form the numbers LMNP and PNML

• LMNP = 1729
• PNML = 9 2 7 1 = 9271

Add them:

1729 + 9271 = 11000

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✅ Final Answer: 11000 ✅

If you'd like the same answer in Telugu, I can give that too.