J P Mohindru and Bharat Mohindru Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 8: EXERCISE

A train which moves with uniform speed for a certain distance takes $6 \mathrm{hours}$less if its speed is increased by $6 \mathrm{km} \mathrm{per} \mathrm{hour},$ it would have taken $6 \mathrm{hours}$ more, had its speed been decreased by $4 \mathrm{km} \mathrm{per} \mathrm{hour}.$ Find the distance of the journey and the speed of the train.

A boat goes $25 \mathrm{km}$  upstream and$33 \mathrm{km}$ downstream in $8 \mathrm{hours}$ it can also go $40 \mathrm{km}$ upstream and $77 \mathrm{km}$ downstream in $15 \mathrm{hours}$. Find the speed of the stream and that of boat in still water.
 

A boat goes $16 \mathrm{km}$  upstream and$24 \mathrm{km}$ downstream in $6 \mathrm{hours}$.It can go $12 \mathrm{km}$ upstream and $36 \mathrm{km}$ downstream in same time. Find the speed of boat in still water and speed of the stream.
  

A man can row $8 \mathrm{km}/\mathrm{h}$​ in still water and he finds that it takes him twice as long to row up as to row down the stream. What is the rate of the stream.

$4$ men and $12$ women can do a piece of work in $3$ days whereas $4$ men and $27$ women can do a piece of work in $2$ days. Find the number of days required to complete the work done by $1$ man or $1$ woman separately.
 

If three taps are opened together for fitting a cistern is filled in $3 \mathrm{hours}$. One of the taps can fill  in $10 \mathrm{hours}$ and another in $15 \mathrm{hours}$.In how much hour does the third tap fill it.
 

A person $\mathrm{A}$ walks a certain distance. Had she walked half a km an hour faster than she did, she would have taken half an hour less, but had she walked half a km an hour slower, she would have taken $40 \mathrm{minutes}$ more. Find the distance and her rate of walking.

A wizard having powers of magical medicines seeing a cock fight going on, spoke privately to both the owners of cocks. To one he said, if your bird wins, then you give me your stake-money, but if you do not win, I shall give you two third of that. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only $12$ gold pieces. Tell me $\mathrm{O}$ Ornament of the first rate Mathematicians, the stake of money each of the cock-owners.