The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son anuj is now. Anuj will be eight years older than Anup is now, when anup is as old as his father. What are their ages now?

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son anuj is now. Anuj will be eight years older than Anup is now, when anup is as old as his father. What are their ages now?

Sol :

Let Anup's present age be x years.
His father's present age = 100 - x.
Therefore, Anup's present age = (100-x)/5 years.

Anup becomes as old as his father is now after (100-2x) years.

Therefore after 100-2x years, we have anup's age = {(100-x)/5 (100-2x)} =(600-11x)/5.

It is given that after 100-2x years, Anuj is 8 years older than his father Anup is now.

Therefore, (600-11x)/5 = x + 8. 
     ==>     600 - 11x    = 5x + 40.
     ==>          600 - 40 =  5x + 11x.
    ==>            560       =  16x
    ==>                     x  =  560/16  = 35.

Hence , Anup's present age be 35 years
His father's present age = 100 - 35 = 65

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Magnetism

Magnetism

The word magnetism is derived from Magnesia, the place where magnetic iron "ORE" was first discovered. Magnet is a substance which possesses the property of attracting small pieces of iron and sets its in North-South direction when suspended freely. The Magnetism is a phenomenon by which this attraction takes place.

Magnetic Poles

If a magnet is dipped into iron filings, it is noted that the fillings cling in tufts, usually at two places in particular i.e. near the ends. Few filings are attracted in the middle of the bar. The places in a magnet where the resultant attractive force appears to be concentrated are called the poles. The pole which points towards the north is called North Pole and other one is called South Pole.

Magnetic and non-magnetic substances

Apart from iron, the only other elements which are attracted strongly by a, magnet are cobalt and nickel. These together with certain strongly magnetic alloys are described as ferromagnetic substances such as copper, brass, wood and glass are not attracted by a magnet and are commonly described as non-magnetic.

or

The substances attracted by magnet are called magnetic substances. The substances not attracted by magnet are called non-magnetic substances.

Magnetic Axis

The magnetic line passing through the north (N) and south (S) poles of a magnet is called the magnetic axis of a magnet.

Magnetic meridian

It is a vertical plane containing the magnetic axis of a freely suspended magnet of a rest under the action of the earth's magnetic field.

Magnetic Equator

It is a line, which is perpendicular bisector of the line joining the two poles of the magnet.
Magnetic Length
It is the distance between the two poles of a magnet. The magnetic length is smaller than geometrical length of the magnet as the poles are not exactly at the ends but situated near the ends a little is side the magnet.

Action of one magnet on another

If N pole of a magnet is brought near N pole of a suspended magnet, the repulsion will occur. Similarly, repulsion will occur between two poles. On the other hand, a N and S pole always attract one another. Thus like poles repel and unlike poles attract.

Test for polarity of a magnet

The polarity of a magnet may be tested by bringing both its poles, in turn, near to the known as poles of a suspended magnet. Repulsion will indicate similar polarity. If attraction occurs, no firm conclusion can be drawn since attraction would be obtained between either (a) two unlike poles or (b) a pole and a piece of unmagnetized material. Thus the repulsion is only sure test for polarity

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