During her 30 km commute to the office, Nadia drove at 120 k

Question

During her 30 km commute to the office, Nadia drove at 120 km/hr until an accident occurred, after which she drove at 30 km/hr. If the commute took 30 minutes, what was her average speed during the last 25 minutes of the commute?

A. 30 km/hr
B. 36 km/hr
C. 42 km/hr
D. 45 km/hr
E. 48 km/hr

A. 30 km/hr
B. 36 km/hr
C. 42 km/hr
D. 45 km/hr
E. 48 km/hr

rajdeep212003 · Answer

I think this one becomes very quick once we directly translate the percentage changes into equations.

Let:

G = original number of gas-powered cars 
E = original number of electric cars

Original total:
G + E

After 10 years:

Gas cars fell by 25% → 0.75G 
Electric cars rose by 50% → 1.5E

The total number of cars increased by 5%, so:

0.75G + 1.5E = 1.05(G + E)

Now expand the right side:

0.75G + 1.5E = 1.05G + 1.05E

Rearranging:

0.45E = 0.30G

So:

E/G = 2/3

That means originally:

Electric : Gas = 2 : 3

Now calculate present numbers:

Electric now:
1.5 × 2 = 3

Gas now:
0.75 × 3 = 2.25

So present ratio becomes:

3 : 2.25

Multiply by 4:

12 : 9 = 4 : 3

Therefore, the present fraction of cars that are electric is:

4 / (4 + 3) = 4/7

Answer: (B) 4/7

I liked this one because the algebra collapses very cleanly once everything is written in terms of the original populations.

— Rajdeep

adconsectetur · Answer

The questions boils down to at what time did the accident occur.

Why last 25 minutes? Did something happen during those 5 minutes? The accident, did it occur after 5 minutes?

Lets say it did occur at 5 minutes.

in 25 minutes  30  km/hr distance covered is 12.5 km. And in 5 minutes @120 km/hr distance covered is 10 km.

Total distance is 30 km.

Hmm, so accident did occur after 5 minutes. Average speed is = (20/25) *60 = 48

Ans E.

Hope it helps.

Mayank_1206 · Answer

Let distance covered before and after the accident be X and 30-X respectively,

T1 and T2 becomes 120/x and (30-X)/30

Now we know that 120/X + (30-X)/30 = 1/2; solving the equation gives us X= 20, and 30-X = 10 kms)

and T1 and T2 becomes 10 mins and 20 mins; we need avg speed for last 25 mins, for 5 mins she drove at 120 kmph and for 20 mins she drove at 30 kpmh, Total distance is 20 kms ( 5/60 *120 + 10 kms ) divided by total time 25 mins ( 5/12) = 48 kmph

Jayneel16 · Answer

So basically you just need to use the tsd table 
let d be the distance for the entire journey
time speed dist
d/120 120 d
d-30/30 30 30-d

we know that the total time taken was 30mins
thus, d/120+d-30/30= 1/2 hrs
solving it would give us 
d=20
 thereby we can get times the person travelled at the different speeds being 10 mins and 20 mins respectively

To find the average speed at which the person was travelling at during the last 25 mins 
we can use the total distance/ total time formula

The person travelled only 5 mins at the speed of 120km/h and the rest at 30km/h

thus, 120*1/12 + 30*20/60

= 20/25 mins

To convert into hrs we get 48 km/h

I know this method is long but i hope it helps you in understanding and visualising the question

During her 30 km commute to the office, Nadia drove at 120 k

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During her 30 km commute to the office, Nadia drove at 120 k

Prep Toolkit

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