Question

'A' starts from Lucknow and 'B' starts from Kanpur to meet each other. Speed of A is 30 km/h, while the speed of Bis 50 km/h. If the distance between Lucknow and Kanpur is 200 km and both A and B start their journey at the same time at what distance from Lucknow do they meet? 70km 75km 80km 85kın 26. A' and 'B' complete a work togather in 8 days.If 'A' alone can do it in 12 days. Then how many day Bwill take to complete the​

Answer 1

Question-1 :

'A' starts from Lucknow and 'B' starts from Kanpur to meet each other. Speed of A is 30 km/h, while the speed of B is 50 km/h. If the distance between Lucknow and Kanpur is 200 km and both A and B start their journey at the same time at what distance from Lucknow do they meet?

Answer :

Let x km be the distance from Lucknow where both A and B meet.

• Speed of A = 30 km/h

Distance travelled by A = x km

• Speed of B = 50 km/h

Distance travelled by B = (200 - x) km

Time taken by both is same.

$\rm time \ taken_A = time \ taken_B$

We know, time = distance/speed

So,

$\rm \dfrac{x}{30}=\dfrac{200-x}{50} \\\\ \rm 50x=30(200-x) \\\\ \rm 50x=6000-30x \\\\ \rm 50x+30x=6000 \\\\ \rm 80x=6000 \\\\ \rm x=6000/80 \\\\ \longrightarrow \bf x=75 \ km$

Therefore, both A and B meet at 75 km from Lucknow.

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Question - 2 :

'A' and 'B' complete a work together in 8 days. If 'A' alone can do it in 12 days. Then how many days B will take to complete the work alone

Answer :

Let B take x days to complete the work alone.

Work done by B in one day = 1/x

A alone can complete the work in 12 days.

Work done by A in one day = 1/12

Both A and B can complete the work in 8 days.

Work done by both A and B in one day = 1/8

Work done by both A and B in one day = Work done by A alone in one day + Work done by B alone in one day

 $\sf \dfrac{1}{8}=\dfrac{1}{12}+\dfrac{1}{x} \\\\ \sf \dfrac{1}{x}=\dfrac{1}{8}-\dfrac{1}{12} \\\\ \sf \dfrac{1}{x}=\dfrac{3-2}{24} \\\\ \sf \dfrac{1}{x}=\dfrac{1}{24} \\\\ \longrightarrow \bf x=24 \ days$

Therefore, B alone can complete the work in 24 days.

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Answer 2

A and B meet at 75 km from Lucknow and  B alone can complete the work in 24 days.

What is the formula of speed distance and time?

• Speed = Distance/Time , This tells us how slow or fast an object moves.
• It describes the distance travelled divided by the time taken to cover the distance.
• Time = Distance / Speed, as the speed increases the time taken will decrease and vice versa.

What do you understand by speed?

• The rate of change of position of an object in any direction.
• Speed is measured as the ratio of distance to the time in which the distance was covered.
• Speed is a scalar quantity as it has only direction and no magnitude.

According to the question:

Let x km be the distance from Lucknow where both A and B meet.

Speed of A = 30 km/h.

Distance travelled by A = x km.

Speed of B = 50 km/h.

Distance travelled by B = (200 - x) km.

Time taken by both is same.

We know, time = distance/speed

So,

$\frac{x}{30}=\frac{200-x}{50} \\ 50 x=30(200-x)\\ 50 x=6000-30 x\\ 50 x+30 x=6000\\ 80 x=6000\\ x=6000 / 80\\ \longrightarrow x=75 \mathrm{~km}$

Therefore, both A and B meet at 75 km from Lucknow.

Again, Let B take x days to complete the work alone.

Work done by B in one day = 1/x

A alone can complete the work in 12 days.

Work done by A in one day = 1/12

Both A and B can complete the work in 8 days.

Work done by both A and B in one day = 1/8

Work done by both A and B in one day = Work done by A alone in one day + Work done by B alone in one day.

$\frac{1}{8}=\frac{1}{12}+\frac{1}{x}\\ \frac{1}{x}=\frac{1}{8}-\frac{1}{12}\\ \frac{1}{x}=\frac{3-2}{24}\\ \frac{1}{x}=\frac{1}{24}\\ \longrightarrow x=24 days$

Therefore, B alone can complete the work in 24 days.

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