The sum of three digit no. And 10times the sum of its digit 496. Find that no.
Answers
Given : Sum of a three digit no. and 10 times the sum of its digit is 496.
To Find : Number
Solution:
Let say 3 digit number is ABC
Value of ABC = 100A + 10B + C
Sum of Digit of ABC = A + B + C
10 times sum of Digits = 10 (A + B + C)
= 10A + 10B + 10 C
sum of 3 digit number and 10times the sum of its digit = 100A + 10B + C + 10A + 10B + 10C
= 110A + 20B + 11C
110A + 20B + 11C = 496
=> 110A + 20B + 10C + C = 496
10(11A + 2B + C) + C = 10 x 49 + 6
=> C = 6
10(11A + 2B + C) = 10 x 49
=> 11A + 2B + C = 49
=> 11A + 2B + 6 = 49
=> 11A + 2B = 43
only possibility is
A = 3 and B = 5 ( as A = 4 => 11A = 44 > 43 , A = 2 => 11A = 22 Hence 2B = 21 but 2B can be maximum 18 )
A = 3
B = 5
C = 6
356 is the number
Verification :
356 = 356 + 10(3 + 5 + 6)
= 356 + 140
= 496
Verified
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Answer:
Step-by-steGiven : Sum of a three digit no. and 10 times the sum of its digit is 496.
To Find : Number
Solution:
Let say 3 digit number is ABC
Value of ABC = 100A + 10B + C
Sum of Digit of ABC = A + B + C
10 times sum of Digits = 10 (A + B + C)
= 10A + 10B + 10 C
sum of 3 digit number and 10times the sum of its digit = 100A + 10B + C + 10A + 10B + 10C
= 110A + 20B + 11C
110A + 20B + 11C = 496
=> 110A + 20B + 10C + C = 496
10(11A + 2B + C) + C = 10 x 49 + 6
=> C = 6
10(11A + 2B + C) = 10 x 49
=> 11A + 2B + C = 49
=> 11A + 2B + 6 = 49
=> 11A + 2B = 43
only possibility is
A = 3 and B = 5 ( as A = 4 => 11A = 44 > 43 , A = 2 => 11A = 22 Hence 2B = 21 but 2B can be maximum 18 )
A = 3
B = 5
C = 6
356 is the number
Verification :
356 = 356 + 10(3 + 5 + 6)
= 356 + 140
= 496
Verified