Question

if cost of 88 articles is A733B. find the value of A and B

Answer 1

Indirectly question is saying " A733B is divisible by 88 , then find value of A and B?"

A733B is divisible by 88 only when it will divisible by 8 and 11.

Divisibility test of 8 :- any number is divisible by 8 when last three digits of number is divisible by 8 . example :- 23872 is divisible by 8 because last three digits 872 is divisible by 8.

divisibility test of 11 :- if sum of even place digits is subtracted from sum of odd place digits of any number and we get integral multiple of 11 then, number is divisible by 11. Example :- 3245682 is divisible by 11
∵ sum of odd place digits = (3 + 4 + 6 + 2) = 15
sum of even place digits = (2 + 5 + 8 ) = 15
sum of odd place digits - sum of even place digits = 0 = 11.0 { integral multiple of 11} hence, 3245682 is divisible by 11.


Now, apply both rule ,
A733B is divisible by 8 when 33B is divisible by 8
This is possible when we take B = 6 [ ∵ 336 is divisible by 8 ]

A733B is divisible by 11 when , (A + 3 + B) - (7 + 3) = 0 or 11
⇒ A + B + 3 - 10 = 0 or 11
⇒ A + 6 + 3 - 10 = 0, 11
⇒ A - 1 = 0 or, 11
⇒ A = 1 or 12 but A ≠ 12 [ because 12 is two digit. ]
so, A = 1 and B = 6

Hence , A = 1 and B = 6