6.Avantika is five years older to her brother Krishna. One year ago, Avantika was twice as old as Krishna. Find the age of Avantika. 7. The sum of the digits of two digit number is 5. If the number is 9 more than the number obtained by interchanging the digits, find the number.
Answers
Answer:
11 years, 32
Step-by-step explanation:
6)Let age of Avantika be x
Age of Krishna = x - 5
Also, x - 1 = 2(x - 6) => x - 1 = 2x - 12 => x = 11
7)Let the number be 10x + y [x is tens place and y is units place]
x + y = 5
Also, 10x + y = 9 + 10y + x => 9x - 9y = 9 => x - y = 1
Solving for x and y, x = 3, y = 2
Therefore the number is 32
Answer:
6. The present age of Avantika is 11 years.
7. Two-digit number is 32.
Step-by-step-explanation:
6.
Let the present age of Avantika be x years.
And the present age of Krishna be y years.
From the first condition,
x - y = 5
⇒ x = y + 5 - - - ( 1 )
From the second condition,
x - 1 = 2 ( y - 1 )
⇒ x - 1 = 2y - 2
⇒ x - 2y = - 2 + 1
⇒ x - 2y = - 1
⇒ y + 5 - 2y = - 1 - - - [ From ( 1 ) ]
⇒ - y + 5 = - 1
⇒ - y = - 1 - 5
⇒ - y = - 6
⇒ y = 6
By substituting y = 6 in equation ( 1 ), we get,
x = y + 5 - - ( 1 )
⇒ x = 6 + 5
⇒ x = 11
∴ The present age of Avantika is 11 years.
7.
Let the digit at the tens place of two-digit number be x.
And the digit at the units place be y.
The original number = 10x + y
The number obtained by interchanging the digits = 10y + x
From the first condition,
x + y = 5
⇒ x = 5 - y
⇒ x = - y + 5 - - ( 1 )
From the second condition,
10x + y = 10y + x + 9
⇒ 10x + y - 10y - x = 9
⇒ 9x - 9y = 9
⇒ x - y = 1 - - [ Dividing by 9 ]
⇒ ( - y + 5 ) - y = 1 [ From ( 1 ) ]
⇒ - y + 5 - y = 1
⇒ - 2y + 5 = 1
⇒ - 2y = 1 - 5
⇒ - 2y = - 4
⇒ 2y = 4
⇒ y = 4 ÷ 2
⇒ y = 2
By substituting y = 2 in equation ( 1 ), we get,
x = - y + 5 - - ( 1 )
⇒ x = - 2 + 5
⇒ x = 3
Two-digit number = 10x + y
⇒ Two-digit number = 10 ( 3 ) + 2
⇒ Two-digit number = 30 + 2
∴ Two-digit number is 32.