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Directions for question 16: This question is based on
the following data.
Three friends - Anil, Bala and Chetan, from X wanted to
travel from town X to town Y which was 40 km. Anil who
had a bike started along with Bala while Chetan started
simultaneously on foot. After some time, Anil dropped Bala
on the way and went back to pick up Chetan while Bala
proceeded to Y on foot. Anil picked up Chetan and reached
Y at the same time as Bala. Anil traveled at
50 km/hr. The speed at which Bala and Chetan walked was
10 km /hr.
16. (i) Find the time after which Anil turned back.
(A) 24 minutes (B) 48 minutes
(C) 36 minutes (D) 30 minutes
Answers
Given : distance 40 km
their walking speeds is 10 kmph
Speed of bike = 50 kmph
Anil who had a bike started along with Bala while Chetan started
simultaneously on foot
Anil dropped Bala on the way and went back to pick up Chetan while Bala
proceeded to Y on foot.
Anil picked up Chetan and reached Y at the same time as Bala
To find : time after which Anil turned back.
What was the entire time involved in travelling
Solution:
Let say after 50x km Anil drop Bala
Time taken = 50x/50 = x hr
Remaining Distance = 40 - 50x km
Time taken by Bala further = (40 - 50x)/10 = 4 - 5x hr
Total time = x + 4 - 5x = 4 - 4x
now after x hrs
Chetan covered Distance = 10x
Distance between Anil and chetan = 50x - 10x = 40x
Time taken to cover 40x by Anil and chetan = 40x/(50 +10) hr
= 2x/3 hr
distance covered by chetan in 2x/3 hr = 20x/3 km
Remaining Distance = 40 - 10x - 20x/3 = 40 - 50x/3 km
Further time taken = (40 - 50x/3)/50 = 0.8 - x/3 hr
Total time = x + 2x/3 + 0.8 - x/3 = 0.8 + 4x/3
4 - 4x = 0.8 + 4x/3
=> 3.2 = 16x/3
=> x = 9.6/16
=> x = 0.6 hrs
=> x = 36 minutes
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