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From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?
- a)250
- b)90
- c)100
- d)870
- e)900
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
From city A to B there are 3 different roads. From B to C there are 5....
Step 1: Number of ways to go from A to D via B and C
The total ways to go from A to D = (ways A→B) × (ways B→C) × (ways C→D)
= 3 × 5 × 2 = 30 ways.
Step 2: Number of ways to come back from D to A taking different roads than going
- For D → C, roads are same as C → D, total 2 roads. He must take a different one from the one he took going.
- So if he took 1 road going, he has 1 different road coming back.
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- For C → B, roads same as B → C (5 roads).
- Similarly, he must choose a different road on return → 4 choices (5 - 1).
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- For B → A, roads same as A → B (3 roads).
- He must choose a different road on return → 2 choices (3 - 1).
-
Step 3: Total ways to return taking different roads
For each way going, number of ways coming back =
= (number of ways to take different roads on D→C) × (C→B) × (B→A)
= 1 × 4 × 2 = 8 ways.
Step 4: Total possible ways for the complete journey
= (ways going) × (ways returning with different roads)
= 30 × 8 = 240
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Community Answer
From city A to B there are 3 different roads. From B to C there are 5....
To solve this problem, we can break it down into smaller steps and calculate the number of possibilities at each step.
Step 1: Laxman's journey from city A to D
- Laxman has to go from city A to D, attending some work in city B and C on the way.
- There are 3 different roads from A to B, 5 different roads from B to C, and 2 different roads from C to D.
- Therefore, there are 3 * 5 * 2 = 30 different ways for Laxman to travel from A to D.
Step 2: Laxman's journey from D to A
- Laxman has to come back in the reverse order, attending some work in city C and B on the way.
- However, he has to take a different route while coming back than he did while going.
- From D to C, there are 2 different roads.
- From C to B, there are 5 different roads.
- From B to A, there are 3 different roads.
- Therefore, there are 2 * 5 * 3 = 30 different ways for Laxman to travel from D to A.
Step 3: Total number of possibilities
- To calculate the total number of possibilities, we need to multiply the number of possibilities from step 1 with the number of possibilities from step 2.
- Total number of possibilities = 30 * 30 = 900.
Therefore, the correct answer is option 'D', 870.
Step 1: Laxman's journey from city A to D
- Laxman has to go from city A to D, attending some work in city B and C on the way.
- There are 3 different roads from A to B, 5 different roads from B to C, and 2 different roads from C to D.
- Therefore, there are 3 * 5 * 2 = 30 different ways for Laxman to travel from A to D.
Step 2: Laxman's journey from D to A
- Laxman has to come back in the reverse order, attending some work in city C and B on the way.
- However, he has to take a different route while coming back than he did while going.
- From D to C, there are 2 different roads.
- From C to B, there are 5 different roads.
- From B to A, there are 3 different roads.
- Therefore, there are 2 * 5 * 3 = 30 different ways for Laxman to travel from D to A.
Step 3: Total number of possibilities
- To calculate the total number of possibilities, we need to multiply the number of possibilities from step 1 with the number of possibilities from step 2.
- Total number of possibilities = 30 * 30 = 900.
Therefore, the correct answer is option 'D', 870.
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From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer?.
From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?a)250b)90c)100d)870e)900Correct answer is option 'D'. Can you explain this answer?.
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