**Worksheet on Word Problems on Ratio and Proportion 1 :**

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

Before look at the problems, if you would like to know the shortcuts on ratio and proportion,

**Problem 1 :**

Find in what ratio will the total wages of the workers of a factory be increased or decreased, if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

**Problem 2 :**

If the angles of a triangle are in the ratio 2:7:11, then find the angles.

**Problem 3 :**

The ratio of two numbers is 7 : 10. Their difference is 105. Find the numbers.

**Problem 4 :**

A , B and C are three cities. The ratio of average temperature between A and B is 11:12 and that between A and C is 9:8. Find the ratio between the average temperature of B and C.

**Problem 5 :**

The ratio between the speeds of two trains is 7:8. If the second train runs 400 miles in 5 hours, then, find the speed of the first train.

**Problem 1 :**

Find in what ratio will the total wages of the workers of a factory be increased or decreased, if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

**Solution :**

Let us assume,

x = No. of workers, y = Average wages per worker

Then, total wages = (no. of workers) x (wages per worker)

Total wages = xy or 1xy ------------ (1)

After reduction in workers in the ratio 15 : 11,

no. of workers = 11x / 15

After increment in wages in the ratio 22 : 25,

wages per worker = 25y / 22

Now, the total wages is

= (11x / 15) ⋅ (25y / 15)

= 5xy / 6

So, the total wages after changes is

= 5xy / 6 ------------ (2)

From (1) and (2) we get that the total wages get decreased from xy to 5xy/6.

So, the decrement ratio is

= xy : 5xy/6

Divide both the terms by "xy".

= 1 : 5/6

Multiply both the terms by 6.

= 6 : 5

Hence, the total wages will be decreased in the ratio

6 : 5

**Problem 2 :**

If the angles of a triangle are in the ratio 2:7:11, then find the angles.

**Solution :**

From the ratio 2 : 7 : 11, the three angles can be assumed to be

2x, 7x, 11x

In any triangle, sum of the angles = 180

So, we have

2x + 7x + 11x = 180°

20x = 180

x = 9

Then, we have

the first angle = 2x = 2 ⋅ 9 = 18°

the second angle = 7x = 7 ⋅ 9 = 63°

the third angle = 11x = 11 ⋅ 9 = 99°

Hence the angles of the triangle are (18°, 63°, 99°)

**Problem 3 :**

The ratio of two numbers is 7 : 10. Their difference is 105. Find the numbers.

**Solution :**

From the given ratio 7 : 10, the two number can be assumed to be

7x, 10x.

Their difference = 105

So, we have

10x - 7x = 105

3x = 105

x = 35

Then we have

the first number = 7x = 7 ⋅ 35 = 245

the second number = 10x = 10 ⋅ 35 = 350

Hence the numbers are 245 and 350.

**Problem 4 :**

A, B and C are three cities. The ratio of average temperature between A and B is 11:12 and that between A and C is 9:8. Find the ratio between the average temperature of B and C.

**Solution :**

From A : B = 11 : 12 and A : C = 9 : 8, we find A in common.

The values corresponding to A in both the ratios are different.

First we have to make them to be same.

Value corresponding to A in the 1st ratio = 11

Value corresponding to A in the 2nd ratio = 9

L.C.M of (11, 9 ) = 99

First ratio ----> A : B = 11 : 12 = (11 ⋅ 9) : (12 ⋅ 9) = 99 : 108

Second ratio ----> A : C = 9 : 8 = (9 ⋅ 11) : (8 ⋅ 11) = 99 : 88

Clearly,

A : B = 99 : 108 ----------- (1)

A : C = 99 : 88 ---------------(2)

Now, the values corresponding to A in both the ratios are same.

From (1) and (2), we get

B : C = 108 : 88

Simplify.

B : C = 27 : 22

Hence, the ratio between the average temperature of B and C is

27 : 22

**Problem 5 :**

The ratio between the speeds of two trains is 7:8. If the second train runs 400 miles in 5 hours, then, find the speed of the first train.

**Solution :**

From the given ratio 7 : 8, we have

speed of the first train = 7x ------(1)

speed of the second train = 8x ------(2)

Second train runs 400 miles in 5 hours (given)

**[Hint : Speed = Distance / Time]**

So, speed of the second train is

= 400/5

= 80 mph ------(3)

From (2) and (3), we get

8x = 80

x = 10

From (1), speed of the first train is

= 7x

= 7 ⋅ 10

= 70

Hence, the speed of the first train is 70 mph.

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 - 2

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