Question

the difference of two natural numbers is 5 and the difference of their reciprocal is 1/10 find the numbers
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Answer 1

ANSWER:

• THE NUMBERS ARE 10 AND 5.

GIVEN:

• Difference of two natural numbers is 5

• Difference of their reciprocal is 1/10

TO FIND:

• The numbers.

ASSUMPTION:

• Let the numbers be x and y

EXPLANATION:

x - y = 5

1/y - 1/x = 1/10

This is beacause 1/y is greater than 1/x as y is less than x

(x - y)yx = 1/10

10 (x - y) = xy

Substitute x - y = 5

5(10) = xy

xy = 50

x = 50/y

Substitute x = 50/y in x - y = 5

50/y - y = 5

(50 - y²) / y = 5

(50 - y²) = 5y

y² + 5y - 50 = 0

Add and subtract by 5y

y² + 5y + 5y - 5y - 50 = 0

y² + 10y - 5y - 50 = 0

y(y + 10) - 5(y + 10) = 0

Take y + 10 as common

(y + 10) (y - 5) = 0

y = 5 as natural number cannot be negative.

Substitute y = 5 in x - y = 5

x - 5 = 5

x = 10

HENCE THE NUMBERS ARE 10, 5

VERIFICATION:

Substitute x = 10 and y = 5 in 1/y - 1/x = 1/10

1/5 - 1/10 = 1/10

(2 - 1)/10 = 1/10

1/10 = 1/10

HENCE PROVED.