Time and Distance and Time and work (UPSC) Part-I

Distance travelled by $Y$ upto 11 a.m. $=2\times 60=120$

Now, at 11 a.m., distance between $X$ and $Y$ $=700-(120+60)=520$ km.hr. Relative speed of $X$ with respect to $Y$

$=60-(-60)=120$ km/hr.

Now, they will cross each other, when they cover a distance of 520 km with a relative speed of 120 km/hr after 11 a.m.

Time taken after 11 a.m. = 520​/120 = 13​/3 × 60 min $=13\times 20=260$ min $=4$ hr. 20 min.

$\therefore$ Time $=11+4$ hr. 20 min $=3:20$ p.m.

Total number of working day $=50\times 50$

$=2500$ days for men

For women it is equal to $4000$ days

For $1$st $10$ day means $40$ men $\times 10=400$ day,

$48$ women $\times 10=480$ days

$2$nd after $10$ days means $35$ men $\times 10=350$ day,

$40$ women $\times 10=400$ days

$3$rd after $10$ day means $30$ men $\times 10=300$ days, $32$ women $\times$ $10=320$ day

s $4$th after $10$ day means $25$ men $\times 10=250$ days, $24$ women $\times$ $10=240$ days

$5$th after $10$ day means $20$ men $\times 10=200$ days, $16$ women $\times$ $10=160$ days

Men $=1500$ days, Women $=1600$ days

1 man = 1.6 women
1600 days of women = 1000 day of men
So, 2500 days need to complete work mean after 50 day
i.e., Man of 1600 working days + woman of 1600 days i.e., 50
days.

Let the time taken by car = C

and the time taken by walking = W

C + W = 6 hrs 45 minutes = 6 × 3/4​ or 27​/4 hrs

C + C = 6 hrs 45 minutes - 2 hrs = 4 hr 45 minutes

or 6× 3/4 −2 hr $=43/4$ hrs

W + W = 2 × 27/4​− 43/4​ hrs

= 54/4 - 19/4 = 35/4 = 8×3/4