In a △ A B C , ∠ A = x ° , ∠ B = 3 x ° and ∠ C = y ° . If 3 y - 5 x = 30 , prove that the triangle is right-angled.

We have to prove that the triangle is right-angled. For this we will prove that one of the angle of the triangle should be 90 ° . Given: ∠ A = x ° , ∠ B = 3 x ° and ∠ C = y ° Sum of three angles in triangle are ∠ A + ∠ B + ∠ C = 180 ° x + 3 x + y = 180 ⇒ 4 x + y = 180 Now, solve the pair of linear equations in two variables 4 x + y = 180 and 3 y - 5 x = 30 So, 4 x + y = 180 ...(i) - 5 x + 3 y = 3 0 …(ii) Multiplying equation (i) by 3 , we get: 12 x + 3 y = 540 …(iii) Subtracting equation (ii) from (iii), we get: 17 x = 5 1 0 x = 510 17 x = 30 ° Substituting x = 30 ° in equation (i), we get: 4 × 30 + y = 180 120 + y = 180 y = 180 - 120 y = 60 ° Angles ∠ A , ∠ B and ∠ C are: ∠ A = x ° = 30 ° ∠ B = 3 x ° = 3 × 30 ° = 90 ° ∠ C = y ° = 60 ° A right-angled triangle is a triangle in which one angle should have a right angle, that is 90 ° . Here, ∠ B = 90 ° Hence, the △ A B C is a right-angled triangle.

MEDIUM

10th CBSE

IMPORTANT

Earn 100

Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

Important Questions on Pair of Linear Equations in Two Variables

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 11

In a

△ A B C, ∠ A = x °, ∠ B = 3 x °

and

∠ C = y ° .

3 y - 5 x = 30,

prove that the triangle is right-angled.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 12

The car hire charges in a city comprised of a fixed charge together with the charge for the distance covered. For a journey of

12 km,

the charge paid is

₹ 89

and the journey of

20 k m,

the charge paid is

₹ 145

. What will a person have to pay for traveling a distance of

30 k m ?

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 13

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student

A

takes foods for

20

days, he has to pay

₹ 1000

as hostel charges whereas a student

B,

who takes food for

26

days, pays

₹ 1180

as hostel charges. Find the fixed charge and the cost of food per day.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 14

Half the perimeter of a garden, whose length is

4

more than its width is

36 m .

Find the dimension of the garden.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 15

The larger of two supplementary angles exceeds the smaller by

18

degrees. Find them.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 16

2

women and

5

men can together finish a piece of embroidery in

4

days, while

3

women and

6

men can finish it in

3

days. Find the time taken by

1

woman alone to finish the embroidery and that taken by

1

man alone.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 17

Meena went to a bank to withdraw

₹ 2000 .

She asked the cashier to give her

₹ 50

and

₹ 100

notes only. Meena got

25

notes in all. Find how many notes

₹ 50

and

₹ 100

she received.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 18

There are two examination rooms

A

and

B .

10

candidates are sent from

A

B,

the number of students in each room is same. If

20

candidates are sent from

B

A,

the number of students in

A

is double the number of students in

B .

Find the number of students in each room.

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Important Questions on Pair of Linear Equations in Two Variables

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