Question

this question is confusing me
The ratio of two numbers is 4:5. After adding 20 to smaller and subtracting 10 from the larger the ratio becomes 14:13. What are the numbers?

Answer 1

Answer:

The ratio of two numbers is 4:5. After adding 20 to the smaller number and subtracting 20 from the greater number the ratio becomes 14:13. Find the numbers.

:

let x = the multiplier

then

4x = the 1st number

and

5x = the 2nd number

:

"After adding 20 to the smaller number and subtracting 20 from the greater number the ratio becomes 14:13."

%284x%2B20%29%2F%285x-20%29 = 14%2F13

Cross multiply

 

14(5x-20) = 13(4x+20)

70x - 280 = 52x + 260

70x - 52x = 260 + 280

18x = 540

x = 540/18

x = 30 is the multipliers

:

Find the the numbers

4(30) = 120 is the first number

and

5(30) = 150 Is the 2nd number

Step-by-step explanation:

Answer 2

$\Huge{\mathfrak{\green{\underline{\red{Solution}}}}}$

Given:

• The ratio of two numbers is 4:5.
• After adding 20 to smaller and subtracting 10 from the larger the ratio becomes 14:13.

To Find:

What are the numbers =?

Solution:

Let's understand

Here,ratio of two numbers is given 4:5 and it is saying that after adding 20 to smaller and subtracting 10 from the larger the ratio becomes 14:13.We have to find rhe numbers.

Let assume:

• Let the first no. be 4x.
• Let the second no. be 5x.

According to the question,

$\sf \implies \: \frac{4x + 20}{5x - 10} = \frac{14}{13} \\ \\ \sf \implies \: 13(4x + 20) = 14(5x - 10) \\ \\ \sf \implies \: 52x + 260 = 70x - 140 \\ \\ \sf \implies \: 70x - 52x = 260 - 140\\ \\ \sf \implies \: 18x=120 \\ \\ \sf \implies \: x = 15$

Hence, The value of x is 15.

Now, put the value to find the numbers.

• Small number = 4x = 4 × 15 = 60
• Large number = 5x = 5× 15 = 75