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.

 10th cbse ncert mathematics chapter 3 pair of linear equations in two variables optional exercise 3.7 for ncert cbse

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. 

x = normal speed of train in km/hr

y = normal time of travel in hours

distance covered = speed * time = xy

If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time

means 

speed = (x+10) 

and time taken = (y-2)

and distance covered = (x+10) * (y-2)

 

if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time

means

speed = (x-10) 

time =(y+3)

and distance =(x-10)*(y+3)

since distance covered is the same 

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

(x-10)*(y+3) = x*y

simplify

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

xy - 2x +10y -20 = xy  

OR 

-2x +10y =20 -------------(1)

 

 

simplify 

(x-10)*(y+3) = x*y 

xy+3x-10y-30 =xy

OR 

3x -10y = 30  -----------------(2)

using elimination method

 

-2x +10y =20 -------------(1)

3x -10y = 30  --------------(2)

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

x           =  50

substitute in -2x +10y =20

-2(50)+10y =20

10y =20+100

10y = 120

y =12 

x =50 km/hr 

y =12 hours

distance travelled =xy = 50*12 = 600 km

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.

x = normal number of rows

y = normal number of students in each row

total number of students = xy

 

If 3 students are extra in a row, there would be 1 row less

means

number of students in each row = (y+3)

number of rows =(x-1) 

total number of students =(x-1)(y+3)

 

If 3 students are less in a row, there would be 2 rows more

means

number of students in each row =(y-3) 

number of rows = (x+2)

total number of students =(x+2)(y-3)

since number of students does not change

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

(x+2)(y-3) = xy

 

simplify

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

xy +3x-1y-3 =xy

3x-y = 3 -------------------(1) 

simplify

(x+2)(y-3) = xy

xy-3x+2y-6=xy

-3x+2y=6 -------------------(2) 

using elimination method

 3x-y = 3 -------------------(1) 

-3x+2y=6 -------------------(2) 

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

        y =9

substitute in 3x-y = 3 

3x -9 = 3

3x = 12

x =4

 

x = 4 rows

y =9 students in each row

 

Total number of students in the class = xy =4*9 = 36

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

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 

 

 

 

  ncert cbse 10th  mathematics chapter 2 optional exercise
 If the zeroes of the polynomial (x^3) – 3(x^2) + x + 1 are a – b, a, a + b, find a and b.
solution
 
2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively
solution



4. If two zeroes of the polynomial (x^4) – 6(x^3) – 26(x^2) + 138x – 35 are 
 [2 ±sqrt(3) ] , find other zeroes

 solution
 
5. If the polynomial (x^4) – 6(x^3) + 16(x^2) – 25x + 10 is divided by another polynomial (x^2) – 2x + k, the remainder comes out to be x + a, find k and a
solution  
 
exercise 2.3
 

3. obtain all other zeroes of 3(x^4)+6(x^3)-2(x^2)-10x-5 if two of its zeroes are sqrt(5/3) and [sqrt(5/3)]
solution
 
4. On dividing (x^3) – 3(x^2) + x + 2 by a polynomial g(x), the quotient and remainder were x – 2
and –2x + 4, respectively. Find g(x).   
solution
 
disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work. Your internet usage may be tracked by the advertising networks and other organizations using tracking cookie and / or using other means