Question

amar travels a certain distance to his office by car everyday and spends rs 60 per day on petrol. the petrol price increases and he calculates for increase of rs 1.5 per km he will be able to cover 2 km less.find the distance from his office to home

Answer 1

Let the distance from office to home = d
The round trip distance, home to office + office to home = 2d
Initial cost per km = 60/2d
New cost per km = 60/2d + 1.5
The number of km that can be covered by rs 60 of petrol at the new cost is
\[\frac{60}{\frac{60}{2d}+1.5}=\frac{60\times 2d}{60+3d}\ km\]
But this distance is 2 km less than the previous distance of 2d. Therefore we obtain the following equation:
\[\frac{60\times 2d}{60+3d}=2d-2\ ...............(1)\]
Equation (1) simplifies to the following quadratic
\[d ^{2}-d-20=0\ ...............(2)\]
The positive solution of quadratic (2) gives the required distance d.

Answer 2

@sheetal.n.iyer Are you able to solve the quadratic? If not please ask for help.

Answer 3

no i am not able to solve it

Answer 4

\[d ^{2}-d-20=0\]
This quadratic can be factorised into the form
(d + ?)(d-?) = 0
The numbers that are shown as question marks are two numbers that when multiplied together = 20 and when subtracted = 1
Can you write the factors of the number 20?
Hint: as an example the factors of 12 are: 1 * 12, 2 * 6 and 3 * 4

Answer 5

@sheetal.n.iyer Do you know any factors of 20?

Answer 6

@sheetal.n.iyer Are you there?

Answer 7

yes

Answer 8

2,10,1,20,4,5

Answer 9

Good work! Notice that 4 and 5 meet the requirement that when multiplied they equal 20 and when subtracted they equal 1. So using these two numbers we get
\[d ^{2}-d-20=(d-5)(d+4)=0\]
Taking the positive solution we get the answer d = 5 kilometers

Answer 10

tnx

Answer 11

You're welcome :)