Question

Distance between P and Q is 72 km. Two men started walking from P and Q at the same time towards each other. The person who started from P traveled uniformly with an average speed 4 kmph. While the other man traveled with varying speeds as follows: In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. Which of the following is true? 1. They meet at 35km from P 2. They meet after 10 hours 3. They meet after 9 hours 4. They meet midway between P & Q 5. both 3 & 4

Answer 1

WHEN BOTH P AND Q STARTED, THEY WILL COVER THE DISTANCE AS UNDER:
DURING FIRST HOUR=4+2=6 KM
DURING 2nd HOUR=4+2.5=6.5 KM
DURING 3rd HOUR=4+3=7 KM  
AND SO ON LIKE 6, 6.5, 7, 7.5, 8, 8.5......... WHICH IS IN THE FORM OF ARITHMETIC SEQUENCE
i.e THEIR SUM=(n/2)(2a+(n-1)d)
IN WHICH WE KNOW SUM=72, a=FIRST TERM=6 AND d=0.5
i.e. 72=(n/2)(2x6+(n-1)0.5)
i.e. 72=(n/2)(12+(n-1)/2)
i.e. 144=(n)(24+n-1)/2
i.e. 288=24n+n^2-n
i.e. n^2+23n-288=0
i.e. EITHER n= -64/2  OR 18/2
BECAUSE n CAN'T BE NEGATIVE 
i.e. n=18/2=9
i.e. P AND Q WILL MEET AFTER 9 HOURS
ALSO 
DISTANCE COVERED BY P AFTER 9 HOURS=9x4=36 KM AND
DIS COVERED BY Q AFTER 9 HOURS=2+2.5+3+3.5.......+6=36 KM 
i.e THEY WILL MEET AFTER 9 HOURS AT THE MIDDLE POINT.

Answer 2

Answer:

They met at half way

Step-by-step explanation:

They moved in 6+6.5+7+7.5+8+8.5+9+9.5+10 = 72

This is an AP with common difference 0.5

Required n.

By formula you get n= 9

hence they met at 9×4 km = 36th Km

Thank You