Question

Q. 31. A train travelling at 65km/hr leaves Bombay at 10 a.m., and another train travelling at 75km/hr
in the same direction leaves Bombay at:12 Noon: How many km: from Bombay will they be
together?
(1) 1050 km (2) 1000 km (3) 975 km
925 km
Hi

Answer 1

Given :-

▪ Train A is travelling at s₁ = 65 km/h leaves Bombay at 10 am , and another train B travelling at s₂ = 75 km/h leaves Bombay at 12 am

To Find :-

▪ How many km from Bombay will they be together?

Solution :-

It is clear that they leave the station with a 2 hour gap. Let us find the relative velocity of the trains.

⇒ Rel. Velocity = 75 - 65

⇒ Rel. Velocity = 10 km/h

Now, Let us find the distance travelled by the train A before train B left, which is equal to the distance travelled in 2 hours by train A.

⇒ Distance travelled, d₁ = 65 × 2

⇒ d₁ = 130 km

Now, Let us find the time after which train B will cover this distance with respect to train A.

⇒ Time taken = 130 / 10

⇒ Time taken = 13 hours

Now, They would meet each after 13 hours as train B leaves Bombay.

So, Distance at which they will meet each other,

⇒ D = d₁ + 65 × 13

⇒ D = 130 + 845

⇒ D = 975 km

Hence, The will meet each other at a distance of 975 Km from Bombay.

So, Option (3) is correct.

Answer 2

GIVEN :-

• A ᴛʀᴀɪɴ ᴛʀᴀᴠᴇʟʟɪɴɢ ᴀᴛ 65km/hr ʟᴇᴀᴠᴇs ʙᴏᴍʙᴀʏ ᴀᴛ 10 a.m. .

• Aɴᴅ ᴀɴᴏᴛʜᴇʀ ᴛʀᴀɪɴ ᴛʀᴀᴠᴇʟʟɪɴɢ ᴀᴛ 75km/hr ɪɴ ᴛʜᴇ sᴀᴍᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ʟᴇᴀᴠᴇs ʙᴏᴍʙᴀʏ ᴀᴛ 12 Noon .

TO FIND :-

• Hᴏᴡ ᴍᴀɴʏ ᴋ.ᴍ. ғʀᴏᴍ ʙᴏᴍʙᴀʏ ᴡɪʟʟ ᴛʜᴇʏ ʙᴇ ᴛᴏɢᴇᴛʜᴇʀ .

SOLUTION :-

✞︎ Hᴇʀᴇ, Rᴇʟᴀᴛɪᴠᴇ Sᴘᴇᴇᴅ ᴄᴏɴᴄᴇᴘᴛ ɪs ᴀᴘᴘʟɪᴇᴅ :-

Fᴏʀ Fɪʀsᴛ Tʀᴀɪɴ :-

• Sᴘᴇᴇᴅ = 65 ᴋm/ʜr

• Jᴏᴜʀɴᴇʏ sᴛᴀʀᴛs ᴀᴛ 10ᴀ.ᴍ. .

☯︎ Bᴜᴛ ᴡʜᴇɴ 12 Nᴏᴏɴ ɪs ʜᴀᴘᴘᴇɴᴇᴅ, ᴛʜᴇɴ ᴛʜɪs ᴛʀᴀɪɴ ʜᴀs ᴛʀᴀᴠᴇʟʟᴇᴅ 2 ʜᴏᴜʀs ᴄᴏᴍᴘʟᴇᴛᴇʟʏ .

☯︎ Hᴇɴᴄᴇ, ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ɪɴ 2 ʜʀ's ɪs,

⟼ Dɪsᴛᴀɴᴄᴇ = Sᴘᴇᴇᴅ × Tɪᴍᴇ

⟼ Dɪsᴛᴀɴᴄᴇ = 65 × 2

⟼ Dɪsᴛᴀɴᴄᴇ = 130 ᴋᴍ.

✰ Tʜᴀᴛ ᴍᴇᴀɴs, ᴛʜᴇ ғɪʀsᴛ ᴛʀᴀɪɴ ɪs ᴛʀᴀᴠᴇʟʟᴇᴅ ᴀʟᴍᴏsᴛ 130 ᴋᴍ. .

✰ Aғᴛᴇʀ ᴛʜᴀᴛ, ᴛʜᴇ sᴇᴄᴏɴᴅ ᴛʀᴀɪɴ ɪs ʟᴇғᴛ ғʀᴏᴍ Bᴏᴍʙᴀʏ .

Sᴏ,

➟ Rᴇʟᴀᴛɪᴠᴇ Sᴘᴇᴇᴅ ᴏғ ᴛᴡᴏ ᴛʀᴀɪɴs = (75 - 65)ᴋᴍ/ʜʀ

➟ Rᴇʟᴀᴛɪᴠᴇ Sᴘᴇᴇᴅ ᴏғ ᴛᴡᴏ ᴛʀᴀɪɴs = 10ᴋᴍ/ʜʀ

Hᴇɴᴄᴇ,

✯ Tʜᴇ sᴇᴄᴏɴᴅ ᴛʀᴀɪɴ sʜᴀʟʟ ᴍᴇᴇᴛ ᴛʜᴇ ғɪʀsᴛ ᴛʀᴀɪɴ ɪɴ,

• $\bf{\implies\:\dfrac{130}{10}}$

• i.e. $\bf\pink{13\:hrs}$

✯ Tʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ғʀᴏᴍ ʙᴏᴍʙᴀʏ ᴡʜᴇʀᴇ ᴛʜᴇʏ ᴡɪʟʟ ʙᴇ ᴛᴏɢᴇᴛʜᴇʀ ɪs,

• $\bf{\implies\:75\times{13}\:}$

• $\bf\purple{\implies\:975\:km\:}$

$\huge\bf\pink{\therefore}$ [3] 975ᴋᴍ. ғʀᴏᴍ ʙᴏᴍʙᴀʏ, ᴛʜᴇʏ ᴡɪʟʟ ʙᴇ ᴛᴏɢᴇᴛʜᴇʀ .