S Purkayastha Solutions for Chapter: Linear Equations in One Variable, Exercise 2: CHECK POINT

The distance between two stations A and B is $230\mathrm{km}$. Two motorcyclists start simultaneously from A and B in the opposite directions and the distance between them after three hours is $20\mathrm{km}$.If the speed of one motorcyclist is less than that of the other by $10\mathrm{km}/\mathrm{hr}$. Find the speed of each motorcyclist.

Three prizes are to be distributed in a quiz contest. The value of the second prize is five-sixth the value of the first prize and the value of the third prize is four-fifth that of the second prize. If the total value of three prizes is $₹150$, then find the value of each prize.

Kamal receives a certain amount of money on her retirement from her employer. She gives half of this money and an additional sum of $₹10,000$ to his daughter. He also gives one-third of the money received and an additional sum of $₹3000$ to his son. If the daughter gets twice as much as the son, find the amount of money Kamal received on her retirement.

Divide$₹1380$ among Aehmad , Johan and Babita, so that the amount Aehmad received is $5$ times as much as Babita share and $3$ times as much as Johan 's share.

Perimeter of a triangle is $49\mathrm{cm}$.One side of the triangle is $7\mathrm{cm}$ longer than another side and $5\mathrm{cm}$ shorter than the third side.Find the length of each side of the triangle.

The length of a rectangle exceeds its breadth by $9 \mathrm{cm}$. If length and breadth are each increased by $3 \mathrm{cm}$, the area of the new rectangle will be$84 {\mathrm{cm}}^2$more than that of the given rectangle. Find the length and breath of the given rectangle.

A steamer goes downstream and covers the distance between two ports in $4$ hours while it covers the same distance upstream in $5$ hours.if the speed of water is $2\mathrm{km}/\mathrm{hr}$, find speed of steamer in still water.

A race boat covers a distance of $66 \mathrm{km}$ Downstream in $110$ Minutes. It covers this distance upstream in $120$ Minutes. The speed of the boat in still water is $34.5 \mathrm{km}/\mathrm{hr}$ .what is the speed of the stream$?$