Question

In New Delhi bus stand an old man namely Aryan was boarded into

a bus to go to his home and he was sitting near to the conductor.

After that two different boys groups also boarded in the same bus.

From the first group(5 members), one of the boy taken 2 tickets to

V.V.M. Colony and 3 tickets to Gandhi Colony, he paid Rs 46.Then

from the second group(8 members) , one of the boy taken 3 tickets

to V.V.M. Colony and 5 tickets to Gandhi Colony and he paid Rs.74.

Aryan calculated the fare from bus stand to V.V.M. Colony and bus

stand to Gandhi Colony correctly by trial and error method but

consumed more time.

From the above data answer the following

i)Which mathematical concept is suitable to calculate fare quickly?

ii) Form a pair of linear equations in two variables?

iii)Find the fare from the bus stand to V.V.M. Colony and

Bus stand to Gandhi Colony?
​

Answer 1

I) elimination method

ii)yes this situation from pair of linear equation in two variables

iiii) let fare from bus statnd to v.v.m colony per person =x

let fare from bustand to gandhinagar per person = y

2x±3y=46

3x ±5y =72

fare from bustand to v.v.m colony=8 rs

fare from bustand to gandhinagar=10 rs

Answer 2

Given : 2 tickets to  V.V.M. Colony and 3 tickets to Gandhi Colony cost Rs 46

3 tickets to  V.V.M. Colony and 5 tickets to Gandhi Colony cost Rs 74

To Find : i) Form a pair of linear equations in two variables?

ii the fare from the bus stand to V.V.M. Colony and  Bus stand to Gandhi Colony?

Solution:

To Form two linear Equation in two variables and solve them is better method than hit & trial method

2 tickets to  V.V.M. Colony and 3 tickets to Gandhi Colony, he paid Rs 46

Let say Each Ticket cost to V.V.M. Colony  = V

& Each Ticket cost to Gandhi . Colony  = G

2V + 3G  = 46  Eq1

3 tickets  to V.V.M. Colony and 5 tickets to Gandhi Colony and he paid Rs.74.

=> 3V + 5G = 74   Eq2

2 & Eq2  - 3 * Eq1

=> 10G - 9G = 148  - 138

=> G  = 10

Substitute value of G in Eq1

=> 2V + 3(10) = 46

=> 2V = 16

=> V = 8

fare from the bus stand to V.V.M. Colony = Rs 8

fare from the bus stand to  Gandhi . Colony  = Rs 10

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