## Ratio Example 3

**Example 1:**

A 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.

**Answer :**

**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 ?

**Answer :**

( 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 ?

**Answer :**

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 ?

**Answer :**

Required probability = ^{5}C_{2} x ^{2}C_{2} / ^{14}C_{4}

= 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 ?

**Answer :**

Required probability = ^{4}C_{2} x ^{2}C_{2} x ^{3}C_{2} / ^{14}C_{8}

= 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 ?

**Answer :**

Required probability = ^{2}C_{2} / ^{14}C_{2} + [ 1 – ^{12}C_{2} / ^{14}C_{2}]

= 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 ?

**Answer :**

Required probability = 1 – ^{11}C_{3} / ^{14}C_{3}

= 1 – 165 / 364

= 199 / 364 .

**Example 8:**

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 none is green ?

**Answer :**

Required probability = ^{10}C_{3} / ^{14}C_{3}

= 30 / 91 .