WORKSHEET ON WORD PROBLEMS ON RATIO AND PROPORTION 1

Worksheet on Word Problems on Ratio and Proportion 1 :

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Worksheet on Word problems on Ratio and Proportion 1 - Questions

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. Worksheet on Word problems on Ratio and Proportion 1 - Questions - Answers

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.

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