Question

Two two-digit numbers are written one after the
other to give a four digit number such that the
larger two digit number is written first.
Now, if the difference of the four digit number
and the sum of two two-digit numbers is 5742
then find the larger 2-digit number.
​

Answer 1

$\bf\huge\underline{\underline{ Given :- }}$

• two 2-digit numbers are written one after other

• one is greater than other. that is written first to form 4-digit number

• Difference between 4 - digit number and sum of 2 - digit number is 5742

$\bf\huge\underline{\underline{ To \: Find:- }}$

• Largest 2 - digit number

$\bf\huge\underline{\underline{ Answer :- }}$

Let the two 2-digit numbers as 10x + y , 10a + b

such that 10x + y > 10a + b

Four digit number

• 100(10x + y) + 10a + b

Sum of 2 digit numbers

• 10x + y + 10a + b

Difference between them ,

• 100(10x + y) + 10a + b - (10x +y + 10a + b) = 5742

• 100(10x + y) + 10a+b - (10x+y) - (10a+b) = 5742

• 100(10x + y ) - (10x + y) = 5742

• (10x + y)(100 - 1 ) = 5742

• (10x + y ) 99 = 5742

• 10 x + y = $\sf\frac{5742}{99}$

• 10x + y = 58

$\rule{10cm}{0.05cm}$

Larger 2 - digit number = 58