Question

The prices of two radios are in the ratio x:y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x:y in its lowest terms.​

Answer 1

Answer:

Case 1

$\frac{x + 20}{y + 20} = \frac{5}{2} \\ 2x + 40 = 5y + 100 \\ 2x - 5y = 60$

Case 2

$\frac{x - 5}{y - 5} = \frac{5}{1} \\ x - 5 = 5y - 25 \\ x - 5y = - 20$

$on \: subtracting \: these \: 2 \: equations \\ x \: = 80 \\ y = 20$

so x : y = 80 : 20 = 4 : 1

Answer 2

Given data:

• The prices of two radios are in the ratio x : y
• When the prices are both increased by £20, the ratio becomes 5 : 2
• When the prices are both reduced by £5, the ratio becomes 5 : 1

To find:

The ratio x : y in its lowest terms

Step-by-step explanation:

Here the ratio is x : y

When the prices are both increased by £20, the new ratio

= x + 20 : y + 20

When the prices are both reduced by £5, the new ratio

= x - 5 : y - 5

By the given conditions,

x + 20 : y + 20 = 5 : 2

⇒ $\dfrac{x+20}{y+20}=\dfrac{5}{2}$

⇒ 2x + 40 = 5y + 100

⇒ 2x - 5y = 60 ... ... (1)

and x - 5 : y - 5 = 5 : 1

⇒ $\dfrac{x-5}{y-5}=\dfrac{5}{1}$

⇒ x - 5 = 5y - 25

⇒ x = 5y - 20 ... ... (2)

Now putting x = 5y - 20 in (1), we get

10y - 40 - 5y = 60

⇒ 5y = 100

⇒ y = 20

Putting y = 20 in (2), we get

x = 100 - 20

⇒ x = 80

Now, x : y

= 80 : 20

= 4 : 1

Final Answer:

Hence x : y = 4 : 1