Class 10 Maths class 10 maths pair of linear equations in two variables

Q 1 :

The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times the number obtained by reversing the order of the digits. Find the number.

(48)

Let the unit’s place digit be $x$ and ten’s place digit be $y$

$∴$ Number = $10 y + x$

According to question,

$x + y = 12$ ...(i)

and $7 (10 y + x) = 4 (10 x + y)$

$x - 2 y = 0$ ...(ii)

Solving (i) and (ii), we get

$x = 8$ and $y = 4$

Hence, the required number is 48

Q 2 :

Find the values of x and y from the following pair of linear equations :

62x + 43y = 167

43x + 62y = 148

(x = 2, y = 1)

62x + 43y = 167 …(i)

43x + 62y = 148 …(ii)

Adding (i) and (ii) and simplifying, we get x + y = 3 …(iii)

Subtracting (ii) from (i) and simplifying, we get x − y = 1 …(iv)

Solving (iii) and (iv) to get x = 2 and y = 1

Q 3 :

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

Let the age of Rashmi = x years

and the age of Nazma = y years

Three years ago, Rashmi’s age = (x – 3)years

Nazma’s age = (y – 3)years

According to question, (x – 3) = 3(y – 3)

⇒ x – 3 = 3y – 9

⇒ x = 3y – 6 ...(i)

Ten years later, Rashmi’s age = x + 10

Nazma’s age = y + 10

According to question, (x + 10) = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x = 2y + 10 ...(ii)

From eqs (i) and (ii), we get 3y – 6 = 2y + 10

⇒ y = 16

Substituting value of y in eq (i), we get

x = 3 × 16 – 6 = 48 – 6 = 42

Thus, the age of Rashmi is 42 years and age of Nazma is 16 years.

Q 4 :

Anuj had some chocolates, and he divided them into two lots A and B. He sold the first lot at the rate of Rs.2 for 3 chocolates and the second lot at the rate of Rs.1 per chocolate, and got a total of Rs.400. If he had sold the first lot at the rate of Rs.1 per chocolate, and the second lot at the rate of Rs.4 for 5 chocolates, his total collection would have been Rs.460. Find the total number of chocolates he had.

(500)

Let the number of chocolates in lot A be x

And let the number of chocolates in lot B be y

$∴$ total number of chocolates = x + y

Price of 1 chocolate = Rs. 2/3 , so for x chocolates = $\frac{2}{3} x$

and price of y chocolates at the rate of Rs.1 per chocolate = y.

$∴$ by the given condition $\frac{2}{3} x + y = 400 \Rightarrow 2 x + 3 y = 1200$ ............ (i)

Similarly, $x + \frac{4}{5} y = 460 \Rightarrow 5 x + 4 y = 2300$ ............. (ii)

Solving (i) and (ii) we get x = 300 and y = 200

$∴$ x + y = 300 + 200 = 500

So, Anuj had 500 chocolates.

Topic Question Set

Q 1 :

The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times the number obtained by reversing the order of the digits. Find the number.

Q 2 :

Find the values of x and y from the following pair of linear equations :

62x + 43y = 167

43x + 62y = 148

Q 3 :

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

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Topic Question Set

Q 1 : The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times the number obtained by reversing the order of the digits. Find the number.

Q 2 : Find the values of x and y from the following pair of linear equations : 62x + 43y = 167 43x + 62y = 148

Q 3 : Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

Want Us to Email you About Special Offers & Updates?

Q 1 :

The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times the number obtained by reversing the order of the digits. Find the number.

Q 2 :

Find the values of x and y from the following pair of linear equations :

62x + 43y = 167

43x + 62y = 148

Q 3 :

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?