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Question
In a three digit number,the digit at hundredth place is three times the digit at once place. if the sum of the digits is 15 and after reversing the digits the number is reduced by 396,find the original number
In a three digit number,the digit at hundredth place is three times the digit at once place. if the sum of the digits is 15 and after reversing the digits the number is reduced by 396,find the original number
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Solution
Let unit digit be x. Then hundred digit will be 3x and tens digit will be 15- (3x + x) = 15 - 4x
So the number is 3x × 100 + (15 - 4x ) × 10 + x = 300x+150 -40x +x = 261 x + 150
When number is reversed , new number will be 100x × (15 - 4x ) × 10 + 3x = 63x + 150
Difference between the number is
261 x + 150 - (63x + 150 ) = 396
⇒198x =396
⇒x= 2.
hundred digit is 3× 2 =6 , tens digit is (15 - 4x )=15 - 8 = 7 and unit digit is 2
Original number is 672.
Let unit digit be x. Then hundred digit will be 3x and tens digit will be 15- (3x + x) = 15 - 4x
So the number is 3x × 100 + (15 - 4x ) × 10 + x = 300x+150 -40x +x = 261 x + 150
When number is reversed , new number will be 100x × (15 - 4x ) × 10 + 3x = 63x + 150
Difference between the number is
261 x + 150 - (63x + 150 ) = 396
⇒198x =396
⇒x= 2.
hundred digit is 3× 2 =6 , tens digit is (15 - 4x )=15 - 8 = 7 and unit digit is 2
Original number is 672.
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