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Let the ten's digit be a and unit's digit of number be (a + 3), and thus number formed be : [10a + (a + 3)]
• According to the Question :
⇒ Number : Sum of digits = 4 : 1
⇒ [10a + (a + 3)] / [a + (a + 3)] = 4 / 1
⇒ [11a + 3] / [2a + 3] = 4 / 1
⇒ 1 × [11a + 3] = 4 × [2a + 3]
⇒ 11a + 3 = 8a + 12
⇒ 11a - 8a = 12 - 3
⇒ 3a = 9
⇒ a = 9/3
⇒ a = 3
- Ten's digit = a = 3
- Unit's digit = (a + 3) = (3 + 3) = 6
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• Number formed will be :
⇢ Number = 10a + (a + 3)
⇢ Number = 10(3) + (3 + 3)
⇢ Number = 30 + 6
⇢ Number = 36
∴ Hence, required number is (3) 36.
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Verification –
L.H.S
⇒ Number : Sum of digits
⇒ [10a + (a + 3)] : [a + (a + 3)]
⇒ [10(3) + (3 + 3)] : [3 + (3 + 3)]
⇒ [30 + 6] : [3 + 6]
⇒ 36 : 9
- Dividing both by 9
⇒ 4 : 1
R.H.S
⇒ 4 : 1
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