Question 102

A three digit number 4a3 is added to another three digit number 984 to give the four digit number 13b7 which is divisible by 11. Then the value of (a+b) is:

Solution

it is given that three digit number 4a3 is added to another three digit number 984 to give the four digit number 13b7 which is divisible by 11

400 + 10a + 3 + 984 = 1300 + 10b + 7

10a - 10 b = -80

b-a=8.....(1)

13b7 is divisible by 11 and hence using its divisibility rule we can say that 9-b will be of the form 11k and hence b can only take 9 value

and so a = 1

a+b = 1+9 = 10

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A three­ digit number 4a3 is added to another three ­digit number 984 to give the four digit­ number 13b7 which is divisible by 11. Then the value of (a+b) is: