Question

Two numbers are in the ratio of 4:7. if 5 is subtracted from each, the ratio becomes 1:2. find the greater number

Answer 1

$\textbf {Hey there, here is the solution.}$

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Ratio : Number 1 : Number 2 = 4 : 7

After subtracting 5:

Ratio : Number 1 : Number 2 = 1 : 2

.

STEP 1: Form equation

Let x be the constant ratio:

$\dfrac{4x - 5}{7x - 5} = \dfrac{1}{2}$

$2(4x - 5) = 7x - 5$

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STEP 2: Solve x:

$2(4x - 5) = 7x - 5$

$8x - 10 = 7x - 5$

$8x - 7x = 10 - 5$

$x = 5$

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STEP 3: Find the numbers:

4x = 4(5) = 20

7x = 7(5) = 35

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Answer: The numbers are 20 and 35

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⭐$\textbf {Cheers}$⭐

Answer 2

According to the Question

${\implies\dfrac{4p-5}{7p-5} = \dfrac{1}{2}}$

8p - 10 = 7p - 5

8p - 7p = 10 - 5

p = 5

Hence

Greater number :-

= 7p

= 7 × 5

= 35