Y 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?

 

Y 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?

cbse ncert 10th mathematics chapter 3 exercise 3.5pair of linear equations in two variables 

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

let x =number of correct answers

and y =number of wrong answers

 

40 marks in a test, getting 3 marks for each right answer and losing 1mark for each wrong answer means

3x-1y=40 ------------------------------------(1)

50 marks , had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer means 

4x -2y =50

dividing by 2

2x -1y =25 ------------------------(2)

 

3x-1y=40 ------------------------------------(1)

2x -1y =25 ------------------------(2)

---------------------------------------------------------subtracting

x =15

substitute in 3x-1y=40

3(15)  - y =40

y =45-40 

y=5

so x =15 correct answers

and y =5 wrong answers

Total number of questions  = x+y = 15 +5 =20

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

 

Let x =speed of the car starting at A in km/hr

and y = speed of the car starting at B in km/hr

 If the cars travel in the same direction at different speeds,they meet in 5 hours.

 

distance = speed *time

so distance travelled by the cars in 5 hours (in the same direction) are

5x km and 5y km respectively

Let the cars meet at a point P when they are travelling in the same direction

Assume that x >y which means that the first car is faster and travels a longer distance in the 5 hours

         100km

*--------------------------*---------------------------------

A                          B                                   P

Clearly AP = 5x  and BP =5y

AP -BP = 100 km using the figure

5x - 5y =100

divide by 5

x -y =20-------------------------(1)

 

If they travel towards each other, they meet in 1 hour 

let the cars meet at Q

As before the first car travels 1x km  and the second car travels 1y km

 

         100km

*----------------*---------*

A                Q         B      

 

AQ=1x 

BQ=1y

 

AQ+BQ = 100 using the figure

1x + 1y =100 ----------------------------(2)

x - y =20-------------------------(1)

x +y =100 ----------------------------(2)

-----------------------------------------------------------------adding

2x  =120

x =60 km/hr

substitute in x +y =100 

y =40 km/hr

 

 

=================================================

ncert cbse 10th mathematics chapter 3 optional exercise 3.7 

 The ages of two friends Ani and Biju differ by 3 years. Ani’s father  is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Ani’s father differ by 30 years. Find the ages of Ani and Biju

solution

 

2. One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? 

solution

3. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. 

solution  

 

4. The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

solution  

5. In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B). Find the three angles.

solution

 

Solve the following pair of linear equations:

 px + qy = p – q 

 qx – py = p + q

solution

 

(ii) ax + by = c
     bx + ay = 1 + c

solution  

 

(iii) 

(x/a) -(y/b) = 0

ax +by = (a^2)  + (b^2)

solution  

 

(iv)

(a – b)x + (a + b) y = (a^2) – 2ab – (b^2)

(a + b)(x + y) = (a^2) + (b^2 )

solution

 

(v)

152x – 378y = – 74

–378x + 152y = – 604

solution   

 ABCD is a cyclic quadrilateral  Find the angles of the cyclic quadrilateral,

if angles are A =(4y+20) , B =(3y-5) , C=(-4x), D=(-7x+5)

solution

 

exercise 3.6

2

Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current. 

solution

 

 (ii) 2 women and 5 men can together finish an embroidery work 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 work, and also that taken by 1 man alone.

solution

 

(iii) 

Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

 

solution

 

exercise 3.5

4

A part of monthly hostel charges is fixed and the remaining depends on the
number of days one has taken food in the mess. When a student A takes food for
20 days she has to pay Rs.1000 as hostel charges whereas a student B, who takes
food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the
cost of food per day.

solution

 

(ii) A fraction changes to (1/3) when 1 is subtracted from the numerator and it changes to (1/4) when 8 is added to its denominator. Find the fraction. 

 solution

(iii)Y 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?

solution 

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

solution 

 

 
 
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