A two digit number is four times the sum of its digits and twice the product of its digits. Find the number.
Answers
✬ Number = 36 ✬
Step-by-step explanation:
Given:
- A two digit number is 4 times the sum of its digits.
- Also it is 2 times the product of its digits.
To Find:
- What is the number ?
Solution: Let ten's digit be x and unit's digit be y. Therefore ,
➟ Sum of digits = x + y
➟ Product of digits = xy
➟ Number = 10 × x + y = 10x + y
A/q
- 10x + y = 4(x + y)
10x + y = 4x + 4y
10x – 4x = 4y – y
6x = 3y
2x = yㅤㅤㅤㅤi
Also ,
- 10x + y = 2xy
10x + y = 2x × 2x
10x + 2x = 4x²
12x = 4x²
12 = 4x
3 = x
Putting the value of x in eqⁿ i
➮ 2 × 3 = y
➮ 6 = y
So ten's digit is 3 and unit's digit is 6. Hence, the number is 36.
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Question :
- A two digit number is four times the sum of its digits and twice the product of its digits.
Required Answer :
- The number is 36.
ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━
Step by step explanation :
Let :
- The ten's digit be m and unit's digit be n.
ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━
- Sum of digits = m + n
- Product of digits = mn
- The Number = 10(m) + n = 10m + n
Atq,
➵ㅤㅤㅤ10m + n = 4(m + n)
➵ㅤㅤㅤ10m - 4m = 4n - n
➵ㅤㅤㅤ6m = 3n
➵ㅤㅤㅤ2m = nㅤㅤㅤㅤㅤㅤ ㅤ[1]
And,
➡ㅤㅤㅤ10m + n = 2mnㅤㅤㅤㅤ[2]
From [1] putting in [2] :
➡ㅤㅤㅤ10m + 2m = 2m × 2m
➡ㅤㅤㅤ12m = 4m²
➡ㅤㅤㅤ12/4 = m²/m
➡ㅤㅤㅤm = 3
Putting value of m in equation [1] :
➢ㅤㅤㅤ2 × 3 = n
➢ㅤㅤㅤn = 6
So, ten's digit = 3 , unit's digit = 6
∴ The number is 36
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