IT BASS+BAS+AS=BTTB what will be the value of T+S+B?
Answers
Question :- if BASS + BAS + AS = BTTB . what will be the value of T + S + B ?
Solution :-
Let us Assume that, each alphabets represent natural numbers from 0 to 9.
So ,
→ BASS = 1000 * B + 100 * A + 10 * S + S
→ BAS = 100 * B + 10 * A + S
→ AS = 10 * A + S
and,
→ BTTB = 1000 * B + 100 * T + 10 * T + B
Putting all these value in LHS and RHS , we have,
→ BASS + BAS + AS = BTTB
→ (1000B + 100A + 10S + S) + (100B + 10A + S) + (10A + S) = (1000B+ 100T + 10T + B)
1000B will be cancel from both sides, re - arranging the rest , we get,
→ 100A + 100B + 10S + 10A + 10A + S + S + S = 100T + 10T + B
→ 100(A + B) + 10(S + 2A) + 3S = 100T + 10T + B
comparing LHS and RHS now, we get,
→ A + B = T ---------- Eqn.(1)
→ S + 2A = T -------- Eqn.(2)
→ 3S = B ---------- Eqn.(3)
From Eqn.(1) and Eqn.(2) now,
→ A + B = S + 2A
→ 2A - A = B - S
→ A = B - S
→ B = (A + S) ------- Eqn.(4)
Putting value of Eqn.(4) in Eqn.(3) ,
→ 3S = B
→ 3S = (A + S)
→ 3S - S = A
→ A = 2S --------- Eqn.(5)
Putting value of Eqn.(3) and Eqn.(5) in Eqn.(1) now,
→ A + B = T
→ 2S + 3S = T
→ T = 5S .
Since , value of T is from 0 to 9.
Therefore,
→ S can be 0 and 1 only. { 5 * 2 = 10 , more than 9. }
if S = 0 ,
→ T = 5S => T = 0
Than,
→ A + B = 0
→ A = (-B) = Not Possible.
Hence,
→ Value of S is = 1 .
Than,
→ T = 5S = 5 * 1 = 5.
Also,
→ B = 3S = 3 * 1 = 3.
∴
☛ T + S + B = 1 + 5 + 3 = 9 (Ans.)
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