Question

The product of two $2$-digit number is $1998.$ If the product of their unit digits is $28$ and that of tens digits is $15,$ find the numbers.

Answer 1

The product of unit digits $=28=7\times 4$

Units digits number are $7\&4$ (Units digits are one-digit numbers)

Now, the product of tens digits $=15=3\times 5$

tens digits number are $3\&5.$ (tens digits are one-digit numbers)

Now, the numbers are either $37\&54or57\&34$

(i) $37\times 54=37\times \left(50+4\right)$

$=37\times 50+37\times 4$ (Distributive property of multiplication over addition)

$$\begin{gathered} =1850+148 \\ =1998 \end{gathered}$$

(i) $57\times 34=34\times \left(50+7\right)$

$=34\times 50+34\times 7$ (Distributive property of multiplication over addition)

$$\begin{gathered} =1700+238 \\ =1938 \end{gathered}$$

It is given that the product of two $2$-digit number $=1998.$

Hence, the required numbers are $37\&54.$