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.
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 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`
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?
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
The difference between an angle and its complement is 10° find measure of the larger angle.
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) | (______, _______) | (______, _______) | ______ |
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
