Question

one fine day Anil started late by half an hour for work by what percentage should he increase his speed to reach office in time if usually takes 2 hours to reach office​

Answer 1

Given :

The hour by which Anil  late for work = half an hour

The usual time taken = 2 hours

To Find :

The percentage by which speed should increase to reach on time

Solution :

The delayed time = 2 hours - 0.5 hour = 1.5 hours

∵ Distance = Speed × Time

Let The usual Speed = S

The delayed speed = s

For late arrival

  D =  s × 1.5                 .............1

For usual arrival

 D = S × 2                    .............2

Or,  From eq 1 and 2

1.5 s = 2 S

i.e   s = $\dfrac{2}{1.5}$ S

So, % increase in speed = $\dfrac{delayed - usual}{usual}$ × 100

                                        = $\dfrac{s-S}{S}$× 100

                                        = $\dfrac{\dfrac{2S}{1.5} -S}{S}$× 100

                                       = $\dfrac{2S-1.5S}{1.5S}$× 100

                                        = 0.33 × 100

                                       = 33 %

Hence, The percentage increase in speed is 33%  . Answer