Find the 5 digit number, 5th digit is one fourth of the 3rd digit and one half of the 4th digit. 3rd digit is one half of the 1st digit. 2nd digit is 5 more than the 5th digit.a)12786b)86421c)46218d)24675Correct answer is option 'B'. Can you explain this answer?

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Answer

To find the 5-digit number, let's break down the given clues one by one:

1. The 5th digit is one-fourth of the 3rd digit and one-half of the 4th digit.
Let's represent the 5th digit as 'A', the 3rd digit as 'B', and the 4th digit as 'C'.
We can write the equation as: A = (1/4)B = (1/2)C

2. The 3rd digit is one-half of the 1st digit.
Let's represent the 1st digit as 'D'.
We can write the equation as: B = (1/2)D

3. The 2nd digit is 5 more than the 5th digit.
Let's represent the 2nd digit as 'E'.
We can write the equation as: E = A + 5

Now, let's substitute the equations into each other to simplify and find the values of the digits:

Substituting equation 2 into equation 1:
A = (1/4)(1/2)D = (1/8)D

Substituting equation 3 into equation 2:
B = (1/2)D

Substituting equation 1 into equation 3:
E = (1/8)D + 5

So, we have:
A = (1/8)D
B = (1/2)D
E = (1/8)D + 5

To find the 5-digit number, we need to find the values of D, B, A, C, and E.

Since B = (1/2)D and A = (1/4)B, we can substitute these values to get:
A = (1/4)(1/2)D = (1/8)D

Therefore, we have:
A = (1/8)D
B = (1/2)D
E = (1/8)D + 5

Now, let's substitute these values into equation 1 to find C:
(1/8)D = (1/2)C
C = (1/4)D

Since E = A + 5, we can substitute the value of A:
E = (1/8)D + 5

Now, let's find the value of D:
Since B = (1/2)D, let's substitute the value of B:
(1/2)D = (1/2)D
D = any value

Once we have the value of D, we can find the values of A, B, C, and E using the equations above.

Looking at the options given, only option b) 86421 satisfies all the given conditions.

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