Ratio Proportion (Class- 7, Experience- 4)

[Exercise- page 103]

E.4.1 The ratio of two numbers is 14 : 25. If the first number is 56, what is the other number?

Solution:

To find the other number, you can set up a proportion.Since the ratio of the two numbers is 14:25, you can set up the equation: 

56 x = 1425 

or, 56 ✕ 25 = 14 ✕ x   [Cross multiply]

or, 1400 = 14x 

or, x = 1400  14 

∴ x = 100   [Divide both sides by 14]

So, the other number is 100. (Answer)

E.4.2 The ratio of the prices of a book and a pen is 7 : 22. If the price of the pen is 32, what is the price of the book?

Solution:

To find the price of the book, we can set up a proportion using the given ratio and the price of the pen. The ratio of the prices of the book and the pen is 7:22. 

Let's denote the price of the book as ( b ). We can set up the proportion:

 b32 =  722

or, 22b = 7 ✕ 32  [cross multiply]

or, 22b = 224

or, b = 224 22 [Divide both sides by 22]

∴ b = 10.18 

So, the price of the book is approximately 10.18 taka. (Answer)

E.4.3 Ratio of the ages of Rocky and Rita is 5 : 27. If Rocky is 10 years old now, how old was Rita 4 years ago?

Solution:

To find Rita's age four years ago, we need to first find Rita's current age using the given ratio and Rocky's current age.

Given that the ratio of their ages is 5:27 and Rocky is currently 10 years old, we can find Rita's current age.

Let Rita's current age is r

We can set up the proportion:

10 r =  527 

or, 5r = 10 ✕ 27  [cross multiply]

or, 5r = 270 

or, r = 270  5   [Divide both sides by 5]

∴ r = 54 

So, Rita is currently 54 years old. To find Rita's age four years ago, we subtract 4 from her current age: 

Rita's age four years ago = 54 - 4 = 50 

Therefore, Rita was 50 years old four years ago. (Answer)

E.4.4 Ratio of the cost of a printer and a computer is 4 : 25. If the cost of the printer is 40000 taka, what is the cost of the computer? If the cost of the printer increases by 25% then what type of the ratio is the cost of printer and computer?

Solution:

To find the cost of the computer, we can use the given ratio and the cost of the printer. 

Given that the ratio of the cost of the printer to the computer is 4:25 and the cost of the printer is 40000 taka, we can find the cost of the computer.

Let's denote the cost of the computer as ( c ).

We can set up the proportion: 

4000   c =  425 

or, 4c = 40000 ✕ 25  [cross multiply]

or, 4c = 1000000 

or, c = 10000000       4   [Divide both sides by 4]

∴ c = 250000 

So, the cost of the computer is 250,000 taka. Now, if the cost of the printer increases by 25%, we need to calculate the new cost of the printer and see the new ratio. 

The cost of the printer after increasing by 25% is:

 New cost of printer = 40000 + (40000 ✕ 0.25) 

or, New cost of printer = 40000 + 10000 

∴ New cost of printer = 50000 taka 

Now, let's find the new ratio:

New ratio =  50000250000 

or, New ratio = 15 

So, after the increase, the new ratio of the cost of the printer to the computer is 1:5. (Answer)

E.4.5 The ratio of the time of coming to school of three friends is 2 : 3 : 4. If the time taken by the first friend to go to school is 18 minutes, what are the times taken by the other two friends to go to school?

Solution:

To find the times taken by the other two friends to go to school, we can use the given ratio and the time taken by the first friend.

Given that the ratio of the time taken by the three friends to come to school is 2:3:4, and the time taken by the first friend is 18 minutes, we can find the times taken by the other two friends.

Let's denote the times taken by the second and third friends as ( x ) and ( y ) respectively. 

We can set up the proportion: 

18 x = 23 

or, 2x = 18 ✕ 3  [cross multiply]

or, 2x = 54 

or, x = 54 2  [Divide both sides by 2]

∴ x = 27 minutes 

So, the time taken by the second friend to go to school is 27 minutes. 

Now, let's find the time taken by the third friend: 

18 y = 24

or, 2y = 18 ✕ 4 

or, 2y = 72 

or, y = 72 2 

∴ y = 36 minutes 

So, the time taken by the third friend to go to school is 36 minutes. (Answer)

E.4.6 In a proportion, if the 1st 2nd, and 4th numbers are 9, 18 and 20 respectively, what is the 3rd number?

Solution:

To find the 3rd number in the proportion, we can use the concept that in a proportion, the product of the means equals the product of the extremes. 

Given: 

1st number: 9 

2nd number: 18 

4th number: 20

Let the 3rd number be ( x ). 

We can set up the proportion: 

 918 =  x20  

or, 9 ✕ 20 = 18 ✕ x  [cross multiply]

or, 180 = 18x 

or, x = 180 18  [Divide both sides by 18]

∴ x = 10 

So, the 3rd number is 10. (Answer)

E.4.7 Rana has 4 pencils and 5 pens. On the other hand, Shajib has 10 pens. Now if the ratios of pencils and pens of Rana and Shajib are proportional, then how many pencils does Shajib has?

Solution:

To find out how many pencils Shajib has, we need to make the ratio of pencils to pens for both Rana and Shajib proportional. 

Given, Rana has 4 pencils and 5 pens, so the ratio of pencils to pens for Rana is 45

Now, we need to find the equivalent ratio for Shajib. Since the ratio of pencils to pens must be the same for both Rana and Shajib. 

Let,  Here ( x ) represents the number of pencils Shajib has, we can set up the proportion: 

45 =  x10  

or, 4 ✕ 10 = 5 ✕ x   [Now, cross multiply]

or, 40 = 5x 

or, x = 40 5  [Divide both sides by 5]

∴ x = 8 

So, Shajib has 8 pencils. (Answer)