**Worksheet on Word Problems on Ratio and Proportion 2 :**

This is the continuity of our web content given on "Word Problems on Ratio and Proportion Worksheet 1".

Before we look at the problems, first let us come to know the shortcuts in ratio and proportion which are required to solve the problems.

**Please click here **to know Ratio and Proportion shortcuts.

**Question 1 :**

Two numbers are respectively 20% and 50% are more than a third number, Find the ratio of the two numbers.

**Question 2 :**

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water ?

**Question 3 :**

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. From the vessel, 10 liters of the mixture is removed and replaced with an equal quantity of pure milk. Find the ratio of milk and water in the final mixture obtained.

**Question 4 :**

If $782 is divided among three persons A, B and C in the ratio 1/2 : 2/3 : 3/4, then find the share of A.

**Question 5 :**

An amount of money is to be divided among P, Q and R in the ratio 3 : 7 : 12. The difference between the shares of P and Q is $2400. What will be the difference between the shares of Q and R ?

**Question 1 :**

Two numbers are respectively 20% and 50% are more than a third number, Find the ratio of the two numbers.

**Answer :**

Let "x" be the third number.

Then, the first number is

= (100+20)% of x

= 120% of x

= 1.2x

The second number is

= (100+50)% of x

= 150% of x

= 1.5x

The ratio between the first number and second number is

= 1.2x : 1.5x

= 1.2 : 1.5

= 12 : 15

= 4 : 5

Hence, the ratio of two numbers is 4 : 5.

Let us look at the next question on "Worksheet on word problems on ratio and proportion 2".

**Question 2 :**

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water ?

**Answer :**

**Vessel A :**

[4:3 ------> 4+3 = 7, M----> 4/7, W----> 3/7]

Let "x" be the quantity of mixture taken from vessel A to obtain a new mixture in vessel C.

Quantity of milk in "x" = (4/7)x = 4x/7

Quantity of water in "x" = (3/7)x = 3x/7

**Vessel B :**

[ 2:3 ------> 2+3 = 5, M----> 2/5, W----> 3/5 ]

Let "y" be the quantity of mixture taken from vessel B to obtain a new mixture in vessel C.

Quantity of milk in "y" = (2/5)y = 2y/5

Quantity of water in "y" = (3/5)y = 3y/5

**Vessel A and B : **

Quantity of milk from A and B is

= (4x/7) + (2y/5)

= (20x + 14y) / 35

Quantity of water from A and B is

= (3x/7) + (3y/5)

= (15x + 21y) / 35

According to the question, vessel C must consist half of the milk and half of the water.

That is, in vessel C, quantity of milk and water must be same.

There fore,

Quantity of milk in (A+B) = Quantity of water in (A+B)

(20x+14y) / 35 = (15x+21y) / 35

20x + 14y = 15x+21y

5x = 7y

x/y = 7/5

x : y = 7 : 5

Hence, the required ratio is 7 : 5.

Let us look at the next question on "Worksheet on word problems on ratio and proportion 2".

**Question 3 :**

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. From the vessel, 10 liters of the mixture is removed and replaced with an equal quantity of pure milk. Find the ratio of milk and water in the final mixture obtained.

**Answer :**

[ 3 : 2 ------> 3+2 = 5, M----> 3/5, W----> 2/5 ]

In 20 liters of mixture,

no. of liters of milk = 20 ⋅ 3/5 = 12

no. of liters of water = 20 ⋅ 2/5 = 8

Now, 10 liters of mixture removed.

In this 10 liters of mixture, milk and water will be in the ratio 3:2.

No. of liters of milk in this 10 liters = 10 ⋅ 3/5 = 6

No. of liters of water in this 10 liters = 10 ⋅ 2/5 = 4

**After removing 10 liters (1st time), **

No. of liters of milk in the vessel = 12 - 6 = 6

No. of liters of water in the vessel = 8 - 4 = 4

Now, we add 10 liters of pure milk in the vessel,

**After adding 10 liters of pure milk in the vessel, **

No. of liters of milk in the vessel = 6 + 10 = 16

No. of liters of water in the vessel = 4 + 0 = 4

After removing 10 liters of mixture and adding 10 liters of pure milk, the ratio of milk and water is

= 16 : 4

= 4 : 1

Hence, the required ratio is 4 : 1.

Let us look at the next question on "Worksheet on word problems on ratio and proportion 2".

**Question 4 :**

If $782 is divided among three persons A, B and C in the ratio 1/2 : 2/3 : 3/4, then find the share of A.

**Answer :**

Given ratio ---> 1/2 : 2/3 : 3/4

First let us convert the terms of the ratio into integers.

L.C.M of denominators (2, 3, 4) = 12

When we multiply each term of the ratio by 12, we get

12 ⋅ 1/2 : 12 ⋅ 2/3 : 12 ⋅ 3/4 ------> 6 : 8 : 9

From the ratio 6 : 8 : 9,

Share of A = 6x

Share of B = 8x

Share of C = 9x

We know that,

Share of A + Share of B + Share of C = 782

6x + 8x + 9x = 782

23x = 782

x = 34

Share of A is

= 6x

= 6 ⋅ 34

= 204

Hence, the share of A = $ 204.

Let us look at the next question on "Worksheet on word problems on ratio and proportion 2".

**Question 5 :**

An amount of money is to be divided among P, Q and R in the ratio 3 : 7 : 12. The difference between the shares of P and Q is $2400. What will be the difference between the shares of Q and R ?

**Answer :**

From the given ratio 3 : 7 : 12,

Share of P = 3x

Share of Q = 7x

Share of R = 12x

Difference between the shares of P and Q is $ 2400

That is,

Share of Q - Share of P = 2400

7x - 3x = 2400

4x = 2400

x = 600

Difference between the shares of Q and R is

= 12x - 7x

= 5x

= 5 ⋅ 600

= 3000

Hence, the difference between the shares of Q and R is $3000.

Apart from the problems given above, if you need more problems on ratio and proportion, please click the following links.

**Ratio and Proportion Worksheet **

**Ratio and Proportion Worksheet - 1**

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on word problems on ratio and proportion 2"

Apart from the stuff given above, if you want to know more about "Word problems on ratio and proportion 2", please click here

Apart from the stuff "Worksheet on word problems on ratio and proportion 2", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**