From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hour. If A traveled with $$\frac{2}{3}$$ of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:
A. 4 km/h
B. 6 km/h
C. 10 km/h
D. 12 km/h
Answer: Option B
Solution(By Examveda Team)
A →_______60Km_________← B Let the speed of A = x kmph and that of B = y kmph According to the question; x × 6 + y × 6 = 60 Or, x + y = 10 --------- (i) And, $$\left( {\frac{{2{\text{x}}}}{3} \times 5} \right) + \left( {2{\text{y}} \times 5} \right) = 60$$ Or, 10x + 30y = 180 Or, x + 3y = 18 ---------- (ii) From equation (i) × 3 - (ii) 3x + 3y - x - 3y = 30 - 18 Or, 2x = 12 Hence, x = 6 kmphAlternate
$$\because $$ They meet after 6 hours if they walk towards each other i.e., their speed will be added.
So, their relative speed in opposite direction
$$ = \frac{{{\text{Distance }}}}{{{\text{Time }}}} = \frac{{60}}{6}$$
Relative speed in opposite direction :
$$\left( \rightleftharpoons \right) = 10{\text{ km/h}}.....{\text{(i)}}$$
According to the question,
$$\eqalign{ & \Rightarrow \frac{2}{3}A + 2B = \frac{{60}}{5} \cr & \Rightarrow \frac{2}{3}A + 2B = 12 \cr & \Rightarrow A + 3B = 18 \cr & \Rightarrow B's{\text{ Speed = }}\frac{{18 - A}}{3} \cr & \Rightarrow A + B = 10 \cr & \Rightarrow A + \frac{{18 - A}}{3} = 10 \cr & \Rightarrow 3A + 18 - A = 30 \cr & \Rightarrow 2A = 12 \cr & \Rightarrow A{\text{'s speed = 6 km/h}} \cr} $$
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Comments ( 4 )
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
I don't understand
plz do shortcut method
6X +6Y = 60
take common 6, and divide 60 by 6.
6(X +Y) = 60
X +Y = 10.
Understand, @Tani ?
HOW DID X+Y=10 COME