Question

Two numbers ratio of 2:3 . If the larger number is 30 more than half of the smaller, find the numbers?

Answer 1

Answer:

Hey mate here your answer

Step-by-step explanation:

Let the 2 numbers be x and y

Sox:y=2:3

3x=2y

y-x/2=30

2y-x=60

3x-x=60

2x=60

x=60/2=30

First number=30

Second Number=30×3/2=45

Please mark me brainliest

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given two numbers in the ratio 2:3
• The larger number is 30 more than half of the smaller

To Find:

• We have to find both the numbers

Solution:

Let the smaller number = 2x

Larger number = 3x

________________________________

$\underline{\large\mathfrak\blue{According \: to \: the \: Question :}}$

$\hookrightarrow \sf{\: Larger \: Number = 30 + \left (\dfrac{Smaller \: Number}{2} \right )}$

Putting their respective values we get

$\hookrightarrow \sf{\: 3x = 30 + \left ( \dfrac{2x}{2} \right ) }$

Now Solving the Equation

$\hookrightarrow \sf{\: 3x = 30 + x }$

$\hookrightarrow \sf{\: 3x - x = 30}$

$\hookrightarrow \sf{\: 2x = 30}$

$\hookrightarrow \sf{\: x = \dfrac{30}{2}}$

$\hookrightarrow \boxed{\sf{x = 15}}$

_______________________________

Therefore:

$\implies \sf{Smaller \: Number = 2 \times 15}$

$\implies \sf{30}$

$\implies \sf{Larger \: Number = 3 \times 15}$

$\implies \sf{45}$

: $\implies \boxed{\mathfrak\red{ \: Larger \: Number = 45}}$

: $\implies \boxed{\mathfrak\red{ \: Smaller \: Number = 30}}$

________________________________

$\huge\mathfrak\green{Verification:}$

$(1)\implies \sf{Ratio = \dfrac{30}{45} = \dfrac{2}{3}}$

$(2)\begin{cases} </p><p>\implies \sf{30 + \left ( \dfrac{Smaller \: Number}{2} \right )} \\ \\ </p><p>\implies \sf{ 30 + \left ( \dfrac{30}{2} \right )} \\ \\</p><p>\implies \sf{30 + 15 } \\ \\</p><p>\implies \sf{45 = Larger \: Number}</p><p>\end{cases}$