Question

Form the greatest and the least number by using each of the digits $2,5,7,3$ and $0$ exactly once. Then find

(a) the sum of two numbers thus formed and

(b) the difference of these numbers.

Answer 1

Step 1 : Form the smallest and greatest number.

Given digits: $2,5,7,3,0$

To find the smallest number using the given digits where each digit occurs only once is to arrange the digits in ascending order and then the number obtained will be the smallest number formed by the given digits.

For the smallest number, $0<2<3<5<7$

So, the smallest number is $20357$ [ $0$ can not be at the right end ]

To find the greatest number using the given digits where each digit occurs only once is to arrange the digits in descending order and then the number obtained will be the greatest number formed by the given digits.

For the greatest number, $7>5>3>2>0$

So, the greatest number is $75320$

Step 2: Find the sum.

Sum $=$greatest number $+$smallest number

$=75320+20357$

So we get,

$\text{TTH}\text{TH}\mathrm{H}\mathrm{T}\mathrm{O}75320+2035795677$

Therefore the sum is $95677$.

Step 3 :Find the difference.

Difference $=$ greatest number $-$ smallest number

$=75320-20357$

So we get,

$\text{L}\text{TTH}\text{TH}\mathrm{H}\mathrm{T}\mathrm{O}41211107\cancel{5}\cancel{3}\cancel{2}\cancel{0}-2035754963$

Hence, the required sum is $95,677$ and difference is $54,963$.