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shutvik [7]
3 years ago
7

One number is four times another number. The sum of their reciprocals is 1/4 . What is the answer

Mathematics
2 answers:
VLD [36.1K]3 years ago
5 0

Answer:

The required numbers are 5 and 20.

Step-by-step explanation:

Given : One number is four times another number.

Let the first number is 'x'

The reciprocal of the first number is \frac{1}{x}

and another number is '4x'

The reciprocal of the another number is \frac{1}{4x}

The sum of their reciprocals is \frac{1}{4}

i.e. \frac{1}{x}+\frac{1}{4x}=\frac{1}{4}

Solving the equation,

\frac{4+1}{4x}=\frac{1}{4}

\frac{5}{4x}=\frac{1}{4}

Cross multiply,

5\times 4=1\times 4x

20=4x

x=\frac{20}{4}

x=5

Another number is 4x=5\times 4=20

Therefore, the required numbers are 5 and 20.

Yakvenalex [24]3 years ago
4 0
Using the information from the question, one can construct two equations:

4 z = x  ...  (1)

\frac{1}{z}  +   \frac{1}{x}   ... (2)

by substituting (1) into (2) to find x

\frac{1}{z} +  \frac{1}{4z}  =   \frac{1}{4}

\frac{5}{4z}  =   \frac{1}{4}

\frac{5}{4z}  =   \frac{1}{4}  

\frac{4z}{5}  =   \frac{4}{1}

\frac{4z}{1}  =   \frac{20}{1}

z =   \frac{20}{4}

⇒ z = 5

By substituting value of z into (1)

⇒ 4 (5) = x

⇒ x = 20

Thus the two numbers are 5 & 20 



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