Latest Capgemini Aptitude Question SOLUTION: 2 men at same tym start walking towards each other from A n B 72 kms apart. sp of A is 4kmph. Sp of B is 2 kmph in 1st hr,2.5 in 2nd, 3 in rd. n so on… when will they meet i in

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2 men at same tym start walking towards each other from A n B 72 kms apart. sp of A is 4kmph. Sp of B is 2 kmph in 1st hr,2.5 in 2nd, 3 in rd. n so on… when will they meet
i in 7 hrs ii at 35 kms from A iii in 10 hrs iv midway

Asked In Capgemini (12 years ago)

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Read Solution (3) :

Soman Mishra  (12 years ago)

After the first hour, they are
4+2=6 km closer to each other. After the second hour, they are
4+2.5=6.5 km closer to each other, and so on. The reduction of distance per hour is therefore an arithmetic progression:
6, 6.5, 7, ...
with initial value a=6 and common difference d=0.5.

The arithmetic series (adding these distances) can be expressed in terms of hours, h, as
S(h) = ah + dh(h-1)/2
= 6h + 0.5(h^2-h)/2
= 6h + (h^2-h)/4
and they meet when this sum equals 72:
6h + (h^2-h)/4 = 72
24h + h^2 - h = 288
h^2 + 23h - 288 = 0
(h - 9) (h + 32) = 0

We have no interest in a negative solution, so the positive one h=9 is the one we want. They meet after 9 hours.

That doesn't match either of the answers that are times, so let's check the distance from A, which at a steady 4 km/h is clearly 36km, half the total distance.

They meet midway (answer iv).

Is this solution Helpfull? Yes (34) | No (4)  

Ajay Sharma  (8 years ago)

Yup.. answer is (iv).
Distance travelled together in each hour is 6+6.5+7+...
this must be equal to 72.
solving this we get total time travelled is 9 hrs.
that is 'A' has travelled 9*4 = 36.
so they meet halfway.

Is this solution Helpfull? Yes (1) | No (1)  

K.Sireesha  (7 years ago)

In one hour two men complete 4+2=6km/h
and in 2nd h 4+2.5=6.5 , in 3rd h-->7 and so on
obtained series is in AP so
by s=a+d(n-1)/2
sh=ah+dh(h-1)/2
here a=6 and d=0.5=1/2
so
6h+0.5h(h-1)/2=72
h^2-23h-288=0
by simplification h=9.

a can reach 36km that is halfway in 9 hours.

Is this solution Helpfull? Yes | No (1)  

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