Advertisements
Advertisements
प्रश्न
The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.
Advertisements
उत्तर
Step 1: Write the conditions as equations
- The sum of the digits is 9: x + y = 9.
- The number obtained by interchanging the digits exceeds the original number by 27: 10y + x = 10x + y + 27.
Step 2: Simplify the second equation
10y + x = 10x + y + 27.
10y − y = 10x − x + 27,
9y = 9x + 27.
y = x + 3
Step 3: Solve the system of equations
- x + y = 9,
- y = x + 3
Substitute y = x + 3 into x + y = 9:
x + (x + 3) = 9
2x + 3 = 9
2x = 6 ⇒ x = 3
Substitute x = 3 into y = x + 3:
y = 3 + 3 = 6
10x + y = 10(3) + 6 = 36.
The two-digit number is 36.
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72
Solve the following system of equations by using the method of elimination by equating the co-efficients.
`\frac { x }{ y } + \frac { 2y }{ 5 } + 2 = 10; \frac { 2x }{ 7 } – \frac { 5 }{ 2 } + 1 = 9`
Solve the following system of linear equations :
2(ax – by) + (a + 4b) = 0
2(bx + ay) + (b – 4a) = 0
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?
Two types of boxes A, B are to be placed in a truck having a capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.
Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?
Solve the following simultaneous equation.
x − 2y = −2 ; x + 2y = 10
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
By equating coefficients of variables, solve the following equations.
3x - 4y = 7; 5x + 2y = 3
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
Complete the activity.
Complete the following table to draw the graph of 3x – 2y = 18.
| x | 0 | 4 | 2 | –1 |
| y | –9 | ______ | ______ | ______ |
| (x, y) | (0, −9) | (______, _______) | (______, _______) | ______ |
The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.
Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.
∴ The number = 10x + y
∴ The number obtained by interchanging the digits = `square`
∴ The sum of the number and the number obtained by interchanging the digits = 132
∴ 10x + y + 10y + x = `square`
∴ x + y = `square` ...(i)
By second condition,
Digit in the ten’s place = digit in the unit’s place + 2
∴ x – y = 2 ...(ii)
Solving equations (i) and (ii)
∴ x = `square`, y = `square`
Ans: The original number = `square`
Solve: 99x + 101y = 499; 101x + 99y = 501
The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm, then find the length of the rectangle.
The semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden.
The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
