NCERT solution Class 10 pair of linear equations in two variables

NCERT Solutions

Class 10 Maths

Pair of Linear Equations in Two Variables

NCERT Questions

Ex. 3.1 Q.1
Ex.3.1 Q.2
Ex.3.1 Q.3
Ex.3.1 Q.4
Ex.3.1 Q.5
Ex.3.1 Q.6
Ex.3.1 Q.7
Ex.3.2 Q.1
Ex.3.2 Q.2
Ex.3.2 Q.3
Ex.3.3 Q.1
Ex.3.3 Q.2

Ex.3.3 Q.2

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

(1) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1.

It becomes if we only add 1 to the denominator. What is the fraction?

(2) Five years ago, Nuri was thrice as old as Sonu.

Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

(3) The sum of the digits of a two-digit number is 9.

Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

(iv) Meena went to bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only.

Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter.

Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days.

Find the fixed charge and the charge for each extra day.

(1) Let the fraction be

According to the question,

(x + 1) ÷ (y – 1) = 1

=> x – y = – 2 ... (1)

+ 1 =

=> 2x – y = 1 ... (2)

Subtracting equation (1) from equation (2), we get

x = 3 ... (3)

Putting this value in equation (1), we get

3 – y = – 2

–y = – 5

y = 5

Hence, the fraction is .

(2) Let the present age of Nuri be = x

Let the present age of Sonu be = y

According to the given information,

(x – 5) = 3(y – 5)

x – 3y = – 10 ... (1)

(x + 10y) = 2(y + 10)

x – 2y = 10 ... (2)

Subtracting equation (1) from equation (2), we get

y = 20 ... (3)

Putting this value in equation (1), we get

x – 60 = – 10

x = 50

Hence, age of Nuri = 50 years and age of Sonu = 20 years.

(3) Let the unit digit and tens digits of the number be x and y respectively.

Then, number = 10y + x

Number after reversing the digits = 10x + y

According to the question,

x + y = 9 ... (1)

9(10y + x) = 2(10x + y)

88y – 11x = 0

–x + 8y =0 ... (2)

Adding equation (1) and (2), we get

9y = 9

y = 1 ... (3)

Putting the value in equation (1), we get

x = 8

Hence, the number is 10y + x = 10 × 1 + 8 = 18.

(4) Let the number of Rs 50 notes and Rs 100 notes be x and y respectively.

According to the question,

x + y = 25 ... (1)

50x + 100y = 2000 ... (2)

Multiplying equation (1) by 50, we get

50x + 50y = 1250 ... (3)

Subtracting equation (3) from equation (2), we get

50y = 750

y = 15

Putting this value in equation (1), we have x = 10

Hence, Meena has 10 notes of Rs 50 and 15 notes of Rs 100.

(5) Let the fixed charge for first three days and each day charge thereafter

be Rs x and Rs y respectively.

According to the question,

x + 4y = 27 ... (1)

x + 2y = 21 ... (2)

Subtracting equation (2) from equation (1), we get

2y = 6

y = 3 ... (3)

Putting in equation (1), we get

x + 12 =27

x = 15

Hence, fixed charge = Rs 15 and Charge per day = Rs 3

Video solution:

Pair of Linear Equations in Two Variables Class 10 Maths NCERT Chapter 3 NCERT Solutions

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