Question

A number is having four digits. The sum of the first and third digit and the sum of the

second and the fourth digit are same. So this number is a multiple of________-------A

The sum is the greatest digit, what is the digit?_________--------B

When the four digit number is divided by A we get BB as the quotient.

To find→ A, B and BB.​

Answer 1

Answer:

101 for a

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Answer 2

Answer:

⇒ Let the 1st, 2nd, 3rd and 4th digits be a,b,c and d respectively.

So, four-digit no. will be dcba

→ According to the given question,

⇒ a+b=c+d --- ( 1 )

⇒ a+d=c --- ( 2 )

⇒ b+d=2(a+c) ---- ( 3 )

∴ a+b=a+2d [ Substituting value of equation ( 2 ) in equation ( 1 ) ]

∴ b=2d --- ( 4 )

⇒ 2d+d=2(a+a+d) [ Substituting eq ( 4 ) and ( 2 ) in eq. ( 3 ) ]

∴ d=4a or a=

4

d

--- ( 5 )

⇒

4

d

+d=c --- [Substituting ( 5 ) in ( 2 ) ]

∴ c=

4

5d

or c=

4d

5

Now d=4a

Since a and d are single digits and we have to form 4 digit no. a<10 and 0<d<10

So, the possible integer values of a and d which satisfy d=4a are

1.a=1,d=4

2.a=2,d=8

∴ The value of d can be either 4 or 8

⇒ When d=4, then c=5.

⇒ When d=8, then c=10.

⇒ But the value of c should be less than 10 as it is a single digit.

∴ Value of c would be 5 which is the third digit of the required number.