**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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