Question

6/ The sum of the digits of a two digit number is 9. The number obtained by interchanging its digits is
9 less than thrice the original number. Find the number.
The speed of the boat in still water is 30 km/h A boat travels for three hours downstream and then​

Answer 1

AnsWer :

27.

SolutioN :

Let,

• Ten place digit be x.
• unit place digit be y.
• Original number 10x + y
• Interchange number 10y + x.

☛ Case 1.

• The sum of the digits of a two digit number is 9.

→ x + y = 9.

$\rule{200}2$

☛ Case 2.

• The number obtained by interchanging its digits is 9 less than thrice the original number. Find the number.

→ 10y + x = 3(10x+y) - 9.

→ 10y + x = 30x + 3y - 9.

→ 7y - 29x = - 9.

$\rule{200}2$

✎ Now, Taking Equation ( 1 )

→ x + y = 9.

→ x = 9 - y _______ ( 3 )

✎ Putting the value of x in Equation ( 2 ) We get.

→ 7y - 29x = - 9.

→ 7y - 29( 9 - y ) = - 9.

→ 7y - 261 + 29y = - 9.

→ 36y - 261 = - 9.

→ 36y = - 9 + 261.

→ 36y = 252.

→ y = 7.

✎ Now, Putting the value of y in Equation ( 3 ) We get.

→ x = 9 - y.

→ x = 9 - 7.

→ x = 2.

✡ So, Number become 10x + y = 10( 2 ) + 7 = 27.