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Product of digits of a 2–digit number is 27. If we add 54 to the number, the new number obtained is a number formed by interchange of the digits. Find the number. (SSC CHSL 2017)
- a)39
- b)93
- c)63
- d)36
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Product of digits of a 2–digit number is 27. If we add 54 to the...
Let digit at ten's place be x and digit at unit's place be y.
∴ The number = 10x + y
When digit are interchanged, the new number
= 10y + x
According to question,
Product of digits = 27 i.e., xy = 27 ...(i)
Also,
10x+ y + 54 = 10y + x
9x – 9y = – 54
x – y = – 6
∴ x = y – 6 ...(ii)
From (i) and (ii),
y (y – 6) = 27
y2 – 6y – 27 = 0
y2 – 9y + 3y – 27 = 0
(y – 9) (y + 3) = 0
∴ y = 9 or y = – 3
∴ x = 3
When x = 3, and y = 9
∴ Required number = 10x + y
= 10 × 3 + 9
⇒ 30 + 9 = 39.
∴ The number = 10x + y
When digit are interchanged, the new number
= 10y + x
According to question,
Product of digits = 27 i.e., xy = 27 ...(i)
Also,
10x+ y + 54 = 10y + x
9x – 9y = – 54
x – y = – 6
∴ x = y – 6 ...(ii)
From (i) and (ii),
y (y – 6) = 27
y2 – 6y – 27 = 0
y2 – 9y + 3y – 27 = 0
(y – 9) (y + 3) = 0
∴ y = 9 or y = – 3
∴ x = 3
When x = 3, and y = 9
∴ Required number = 10x + y
= 10 × 3 + 9
⇒ 30 + 9 = 39.
Most Upvoted Answer
Product of digits of a 2–digit number is 27. If we add 54 to the...
The product of the digits of a 2-digit number can vary depending on the specific number.
For example, if the number is 24, the product of the digits would be 2 * 4 = 8.
If the number is 56, the product of the digits would be 5 * 6 = 30.
Therefore, the product of the digits of a 2-digit number is not a fixed value and can be different for different numbers.
For example, if the number is 24, the product of the digits would be 2 * 4 = 8.
If the number is 56, the product of the digits would be 5 * 6 = 30.
Therefore, the product of the digits of a 2-digit number is not a fixed value and can be different for different numbers.
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Product of digits of a 2–digit number is 27. If we add 54 to the number, the new number obtained is a number formed by interchange of the digits. Find the number. (SSC CHSL 2017)a)39b)93c)63d)36Correct answer is option 'A'. Can you explain this answer?
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