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 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:

Answer: Option B

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 kmph

Alternate

$$\because$$ 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,
$$\begin{array}{rl}& \Rightarrow \frac{2}{3}A+2B=\frac{60}{5}\\ & \Rightarrow \frac{2}{3}A+2B=12\\ & \Rightarrow A+3B=18\\ & \Rightarrow B^{\prime }s\text{ Speed = }\frac{18-A}{3}\\ & \Rightarrow A+B=10\\ & \Rightarrow A+\frac{18-A}{3}=10\\ & \Rightarrow 3A+18-A=30\\ & \Rightarrow 2A=12\\ & \Rightarrow A\text{’s speed = 6 km/h}\end{array}$$