Question

A 5 digit number 21a35 is added to another 5-digit number 29096 to give a 5-digit number 503b1 which is divisible by 11. what is b-a

Answer 1

Answer:

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Step-by-step explanation:

abcde is a 5 digit no. 

∴abcde=10000a+1000b+100c+10d+e (1)

 because, abcde1=3×1abcde

So,=>100000a+10000b+1000c+100d+10e+1=3×(100000+10000a+1000b+100c+10d+e)

=>100000a+10000b+1000c+100d+10e+1=300000+30000a+3000b+300c+30d+3e

=>100000a+10000b+1000c+100d+10e−30000a−3000b−300c−30d−3e=300000−1

=>70000a+7000b+700c+70d+7e=299999

=>7(10000a+1000b+100c+10d+e)=7(42857)

=>10000a+1000b+100c+10d+e=42857

Putting value from 1 we get

abcde=42857 

sum of digits = 4+2+8+5+7

                =26

Answer 2

The answer is 7

GIVEN

A 5 digit number 21a35 is added to another 5-digit number 29096 to give a 5-digit number 503b1 which is divisible by 11.

TO FIND

The value of b-a

SOLUTION

We can simply solve the above problem as follows;

Let us first observe the final number that is; 503b1.

It is given that 503b1 is divisible by 11.

We know that number is divisible by 11 if the difference between the sum of digits in even places and sum of digits at odd places is either a multiple of 11 or 0.

Therefore,

(5+3+1) - (0+b) = 9-b = 0 (multiple of zero is zero)

b = 9

Therefore, The number is 50391

Now,

50391 is obtained by adding 21a35 to 29096

29096 + 21a35 = 50391

21a35 = 50391-29096 = 21295

Comparing LHS to RHS

21a35 = 21295

a = 2

Now,

b-a = 9-2 = 7

Hence, The answer is 7

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