Question

one number is four times another. the sum of their reciprocal is 5/12. what are the two number​

Answer 1

Assume;

One number = a

Another number = 4a

Sum of reciprocal = 5 / 12

So,

1/a + 1/4a = 5 / 12

[4a + a] / 4a² = 5 / 12

[5a] / 4a² = 5 / 12

5 / 4a = 5 / 12

20a = 60

a = 3

One number = a = 3

Another number = 4a = 4(3) = 12

Answer 2

Answer:

3 & 12

Step-by-step explanation:

As per the question,

let x = 4y

$\frac{1}{x} + \frac{1}{y} = \frac{5}{12}$

Putting x = 4y in above equation,

$\frac{1}{4y} + \frac{1}{y} = \frac{5}{12} \\ ⇒ \: \frac{1 + 4}{4y} = \frac{5}{12} \\ ⇒ \: 4y = 12 \\ ⇒ \: y = 3$

And, x = 4y = 4 × 3 = 12

So, the required two numbers are 3 & 12.

Hope it helps!

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