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Question

A passenger is allowed some free luggage by Rajdhani express. Two passengers have a total of 105kg luggage and they have to pay Rs.18 and Rs.12 as luggage charges respectively. If one passenger having the same kg of luggage then he would have to pay Rs.36, find how much free luggage each passenger is allowed to carry.

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Solution

Let the free luggage allowed be x kg and the charge paid for each kg more than x=Rs.y
Then according to the question,
105kgTwo passengers have a total of 105kg luggage and they have to pay Rs.18Rs.18 and Rs.12 with some x kg as free luggage .Rs.12
y(105(x+x))=12+18
1052x=30y(i)
Also, If one passenger having the same kg of luggage then he would have to pay Rs.36, therefore,
y(105x)=36
105x=36y(ii)

Multiplying (i) by 36 and (ii) by 30 we get,
378072x=1080y315030x=1080y+63042x=042x=630

x=63042=15

Free luggage allowed =15 kg
From (i) we get,
1052(15)=30y
10530=30y
y=3075=0.4
y=Rs.0.40=40 paise

Let us check (ii)
y(105x)=30
0.4(10515)=0.4(90)
=36


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