Question

Two numbers are in the ratio 5:4. If 3 is subtracted from the first and 2 is subtracted from the second, they will be
in the ratio 6:5. Find the numbers.

Answer the question and I will mark u brainliest ​

Answer 1

Given :

• Two numbers are in the ratio 5:4.
• If 3 is subtracted from the first and 2 is subtracted from the second, they will be in the ratio 6:5.

To find :

• The two numbers.

Solution :

Consider,

• 1st number = 5x
• 2nd number = 4x

According to the question :-

• If 3 is subtracted from the first and 2 is subtracted from the second, they will be in the ratio 6:5.

$\to\sf{(5x-3):(4x-2) =6:5}$

$\to\sf{\dfrac{5x-3}{4x-2}=\dfrac{6}{5}}$

$\to\sf{25x-15=24x-12}$

$\to\sf{25x-24x=15-12}$

$\to\sf{x=3}$

Therefore,

• 1st number = 5×3 = 15
• 2nd number = 4×3 = 12

Therefore, the two numbers are 15 and 12.

__________________

Verification :-

• 1st number = 15
• 2nd number = 12

According to the question :-

• If 3 is subtracted from the first and 2 is subtracted from the second, they will be in the ratio 6:5.

$\implies\sf{(15-3):(12-2)=6:5}$

$\implies\sf{12:10=6:5}$

$\implies\sf{6:5=6:5}$

Hence Verified !

Answer 2

✯✯ QUESTION ✯✯

Two numbers are in the ratio 5:4. If 3 is subtracted from the first and 2 is subtracted from the second, they will be in the ratio 6:5. Find the numbers.

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✰✰ ANSWER ✰✰

$\implies\tt{Let\:first\:no.\:be=5x}$

$\implies\tt{Let\:Second\:no.\:be=4x}$

➥A.T.Q : -

If 3 is subtracted from first(5x) and 2 is subtracted from second(4x)...Then,they will be in the ratio 6:5....

➥Now ,

$\implies\tt{(5x-3):(4x-2)=6:5}$

$\implies\tt{\dfrac{5x-3}{4x-2}=\dfrac{6}{5}}$

$\implies\tt{5(5x-3)=6(4x-2)}$

$\implies\tt{25x-15=24x-12}$

$\implies\tt{25x-24x=-12+15}$

$\implies\tt{1x=3}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{3}}}$

➥So ,

$\implies\tt\bold{First\:Number=5(3)}$

$\implies\tt{15}$

$\implies\tt\bold{2nd\:Number=4(3)}$

$\implies\tt{12}$