In a two digit number, the product of digits is 20 and their difference is 1. (a) Write the standard form of a number of two digits. [1] (b) Find the number. [3]

(a) Standard form of a two‑digit number

Let the tens digit be $x$ and the units digit be $y$.
The number can be expressed as

$$\text{Number}=10x+y$$

where $x$ and $y$ are integers satisfying $1\le x\le 9$ and $0\le y\le 9$.

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(b) Finding the number

The conditions given are

• Product of the digits: $xy=20$
• Difference of the digits: $x-y=1$  (the tens digit is larger)

Step 1 – List factor pairs of 20 that can be digits

Only the pairs where both $x$ and $y$ are single‑digit numbers (0–9) are admissible. Hence the viable pairs are $(4,5)$ and $(5,4)$.

Step 2 – Apply the difference condition

The required difference is $x-y=1$.
Checking the two admissible pairs:

• For $(4,5)$: $4-5=-1$ (does not satisfy)
• For $(5,4)$: $5-4=1$ (satisfies)

Thus the correct digit pair is $x=5$ and $y=4$.

Step 3 – Form the number

Using the standard form $10x+y$:

$$\text{Number}=10(5)+4=50+4=54$$

Hence, the two‑digit number whose digits have product 20 and differ by 1 is 54.