Written Problems Involving Equivalent Ratio

Q(i):- The ratio of profit to cost price on sales at DeeDee's is 3 : 5

Find the cost price of a skirt if the sales profit is £30?

First lets look at the question:-

First we have the ratio of profit to cost so we'll write this in ratio format P : C

Next the question tells us that it is in the ratio of 3 : 5

We have been asked to find the cost price and we've been told the profit is £30

A(i):-Therefore we can write the information we've been given as follows;

P : C

3 : 5

30 : ?

The 3 has turned into 30 so we will have to divide;

30 ÷ 3 = 10 (Now we must multiply the 5 X 10)

10 X 5 = 50

Therefore the cost price for the skirt is £50

 

(ii):- A type of concrete requires a mixture of sand, cement and grit in the ratio 4 : 1 : 2 , if 14 buckets of sand are used what are the quantities of cement and grit required?

We have the ratio of sand, cement and grit, so let's write this in ratio format

S : C : G

Next the question tells us these items are in the ratio of 4 : 1 : 2

We are told that 14 buckets of sand are used

We've been asked to find the quantities of cement and grit required

A(ii):-Therefore we can write the information we've been given as follows;

S : C : G

4 : 1 : 2

14 : ? : ?

We've went from 4 to 14 so we'll divide 14 ÷ 4 = 3.5(now we must multiply the 1 and the 2 by 3.5)

1 X 3.5 = 3.5 (cement)

2 X 3.5 = 7 (grit)

So to answer the question how much cement and grit is needed we see there is;

Cement 3.5 buckets and

Grit 7 buckets required.

 

 

NOW TO DIVIDE THE QUANTITIES IN A GIVEN RATIO:-

Q(i):- Divide £400 between John and Simon in the ratio 1 : 4

A(i):- J : S

          1 : 4 = 5 parts

JOHN: ¹/₅ x 400 = £80 that is (400 ÷ 5 = 80)

SIMON: ⁴/₅ x 400 = £320 that is ( 400 ÷ 5 = 80 then multiply the 80 x 4 = 320)

JOHN gets £80 and SIMON gets £320.

 

Q(ii):- The three angles in a triangle are in ratio 1 : 2 : 3, Find the size of each of the angles?

A(ii):- All the angles in a triangle add up to 180 degrees.

1 : 2 : 3 = 6 parts

Angles: the first angle we will look at is the 1 part out of the 6 parts, so as a fraction it would be ¹/₆ (one sixth)- therefore it will be ¹/₆ of the 180 degrees.

180 ÷ 6 = 30 degrees

The next angle is represented by the 2 parts out of the 6 parts, so as a fraction it would be ²/₆(two sixths)which is equivalent to a ¹/₃(one third) - therefore this angle will be¹/₃ of the 180 degrees.

180 ÷ 3 = 60 degrees

The last angle is represented by the 3 parts out of the 6 parts, so as a fraction it would be ³/₆ (three sixths) which is equivalent to a ¹/₂ ( a half ) - therefore this angle will be ¹/₂ of the 180 degrees.

180 ÷ 2 = 90 degrees

As an extra measure to check the sum of the degrees add them up;

30 + 60 + 90 = 180

Therefore the calculations are correct.

The size of the angles are 30 , 60 , and 90 degrees.

 

Q(iii):- A piece of rope is 60cm long and is cut into three pieces in the ratio 4 : 1 : 5

Find the length of the shortest piece?

A(iii):- 4 : 1 : 5 = 10 parts

The shortest piece is represented by the 1 part;

Therefore ¹/₁₀ x 60 = 6cms

The shortest piece is 6cms in length