ayushi covered 2/5 of her journey by scooty,1/3 by train and rest by car. what fraction of her journey was covered by car
Answers
ʏᴇs, 10ᴋ ɪs 6.2 ᴍɪʟᴇs; ᴀ ᴄᴏɴsɪᴅᴇʀᴀʙʟᴇ ᴅɪsᴛᴀɴᴄᴇ.
ʟᴇᴛ x = ᴛᴏᴛᴀʟ ᴊᴏᴜʀɴᴇʏ ᴅɪsᴛᴀɴᴄᴇ
ʙʏ ᴛʀᴀɪɴ + ʙʏ ᴛᴀxɪ + ʙʏ ʙᴜs + ʙʏ ғᴏᴏᴛ = ᴛᴏᴛᴀʟ ᴊᴏᴜʀɴᴇʏ
(2/5)x + (1/3)x + (1/6)x + 10ᴋ = x
ᴛᴏ ɢᴇᴛ ʀɪᴅ ᴏғ ᴀʟʟ ғʀᴀᴄᴛɪᴏɴs, ᴍᴜʟᴛɪᴘʟʏ ʙʏ ᴛʜᴇ ʟᴄᴍ ᴏғ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀs (ᴛʜɪs ɪs ᴊᴜsᴛ ʟɪᴋᴇ ғɪɴᴅɪɴɢ ᴛʜᴇ ʟᴇᴀsᴛ ᴄᴏᴍᴍᴏɴ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ). ʟᴄᴍ = 30
12x + 10x + 5x + 300ᴋ = 30x
27x + 300ᴋ = 30x [ɢʀᴏᴜᴘ ʟɪᴋᴇ ᴛᴇʀᴍs]
300ᴋ = 3x [sᴜʙᴛʀᴀᴄᴛ 27x ғʀᴏᴍ ʙᴏᴛʜ sɪᴅᴇs]
100ᴋ = x [ᴅɪᴠɪᴅᴇ ʙᴏᴛʜ sɪᴅᴇs ʙʏ 3]
Answer:
Let the length of his total journey be x
So,
5
2
x+
3
1
x+
4
1
x+3=x
solving
x(
5
2
+
3
1
+
4
1
)−x=−3
=x(
5
2
+
3
1
+
4
1
−1)=−3
=x(
60
2×12+20+1×15−60
)=−3
=x(
60
24+20+15−60
)=−3
=x(
60
−1
)=−3
=
60
x
=3
∴x=180 km