## Ratio Example 3

### Example 1:

money bag contains 50 p, 25 p, and 10 p coins in the ratio 5 : 9 : 4, and the total amounting to Rs.206.
Find the individual number of coins of each type.
Step 1: Let the number of 50 p ,25 p, and 10 p coins be 5x, 9x, 4x respectively.
Then, 5x / 2 + 9x / 4 + 4x / 10 = 206
= 50x + 45x + 8x = 4120
= 103x = 4120
= x = 40.
Step 2: Number of 50 p coins is ( 5 x 40 = 200 ),
Number of 25 p coins is( 9 x 40 = 360 ),
Number of 10 p coins ( 4 x 40 = 160 ),

### Example 2:

On a self there are 4 books on Economics , 3 books on Management and 4 books on Statistics . In how many different ways can be the books be arranged so that the books on Economics  are kept together ?
( 4 books on Statistics ! + 3 books on Management ! + 1 x   4 books on Economics ! )
Total ways = 8! x 4!
= ( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) x ( 4 x 3 x 2 x 1 )
= 40320 x 24
= 967680 .
So , we can 967680 way be the books be arranged .

### Example 3:

How many bags are required for filling 1824 kg of wheat if each bag filled with 152 kg of wheat ?
Each bag filled means 1 bag filled with 152 kg  .
Total kg of wheat is 1824 kg , So we divide it  by each bag filled with 152 kg
Number of bags = 1824 / 152
= 12 .

### Example 4:

An urn contains 4 green , 5 blue , 2 red  and 3 yellow marbles . If four marbles are drawn at random , what is the probability that two are blue and two are red ?

Required probability = 5C2 x 2C2 / 14C4
= 10 / 1001 .

### Example 5:

An urn contains 4 green , 5 blue , 2 red  and 3 yellow marbles . If eight marbles are drawn at random , what is the probability that there are equal number of marbles of each color ?

Required probability = 4C2 x 2C2 x 3C2 / 14C8
= 180 / 3003 = 60 / 1001 .

### Example 6:

An urn contains 4 green , 5 blue , 2 red  and 3 yellow marbles . If two marbles are drawn at random , what is the probability that both are red or at least one is red ?

Required probability = 2C2 / 14C2 + [ 1 – 12C2 / 14C2]
= 1 / 91 + [ – 66 / 91 ]
= 1 / 91 + 25 / 91
= 26 / 91 .

### Example 7:

An urn contains 4 green , 5 blue , 2 red  and 3 yellow marbles . If three marbles are drawn at random , what is the probability that at least one is yellow ?