Question

ncert maths ex-3.6 q-2(iii)

(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4
hours if she travels 60 km by train and the remaining by bus. If she travels 100 km
by train and the remaining by bus, she takes 10 minutes longer. Find the speed of
the train and the bus separately.

step by step......​

Answer 1

then sum of n-1 terms= 3(n-1)2+5(n-1)

So nth term of A.P will be Tn=3n2+5n- 3(n-1)2-5(n-1)= 3n2+5n-3n2-3+6n-5n+5=6n+2

in this way by putinng values of n= 1,2,3,4,5,6,7,_______n-1, n

we will get the AP as 8,14,20,26,32,38,44,____and the 16th term will be= 6*16+2=98

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Answer 2

the speed of train be x km/hr and that of bus is y km/hr.

so acc to ques. and using D=S/T

60/x+240/y=4........(1)

100/x+200/y=25/6.....(2)

now put 1/x=u and 1/y=v

60u+240v=4

15u+60v=1......(3)

100u+200v=25/6

u+2v=1/24......(4)

multiplying (4) by 15

15u+30v=5/8......(5)

subtracting (5) from (3)

30v=3/8

v=1/80    this implies y=1/v=80km/hr

put v=1/80 in (4)

u+2*1/80=1/24

u+1/40=1/24

u=1/24-1/40

u=2/120

u=1/60  this implies x=1/u=60 km/hr

hence speed of train=60km/hr and that of bus =80km/hr

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