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 1000 as hostel charges whereas a student B, who takes food for 26 days, pays 1180 as hostel charges. Find the fixed charges and the cost of food per day.

 cbse ncert 10th mathematics chapter 3 exercise 3.5

pair of linear equations in two variables

 

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.

 

let x = fised charges for a month

and y = charge of food per day 

 

student A takes food for 20 days has to pay Rs.1000 means

x + 20y =1000 ----------------------(1)

 

student B, who takes  food for 26 days, pays Rs.1180 means

x +26 y =1180 ---------------------(2)

x + 20y =1000 ----------------------(1)

x +26 y =1180 ---------------------(2)

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

(-6)y =-180

y = 30

substitute y =30 in x + 20y =1000

x+20(30)  =1000

x =1000 - 20*30

x=400

fixed charge =Rs.400 /- per month

charge for food = Rs.30 /- per day

(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.

let fraction =(x/y)

 

fraction changes to (1/3) when 1 is subtracted from the numerator means

[(x-1)/y] =(1/3)

3(x-1) = 1y

3x-3 = y

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

fraction changes to (1/4) when 8 is added to its denominator means

[x /(y+8)] =(1/4)

4x =1(y+8)

4x=1y+8

4x-1y =8-----------------(2)

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

4x-y =8-------------------(2)

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

(-1)x =(-5)

x = 5

substitute x=5 in 3x-y=3

3(5)-y=3

(-y)= 3-15

(-y)= =(-12)

y=12

fraction = [5/12]

 

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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

 
 
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