Question

Sum of two numbers is 30 and the sum of their reciprocal is 3/20

Answer 1

Answer:

10,20

Step-by-step explanation:

Let the numbers be a,b.

a+b=30 - 1

1/a +1/b=3/20 - 2

• b/ab+a/ab=(a+b)/ab=3/20

• 30/ab=3/20

• ab=30 * 20 /3

• ab=200

• a=200/b

Substituting this in 1 we get,

• 200/b+b=30 =  (200+b^2)/b=30  =b^2- 30b +200

Solving this quadratic equation we get

     b=10 or 20

Therefore when one number is 10 the other is 20.

a=10,b=20

Answer 2

The required two numbers are 10 and 20.

Question: The Sum of two numbers is 30 and the sum of their reciprocal is 3/20 find the two numbers.

10,20

Given:

• The Sum of the two numbers is 30.
• The sum of their reciprocal is 3/20.

To find:

The two numbers.

Solution:

Let the required numbers be p and q.

Sum of the numbers is 30 and it can be mathematically presented as,

p+q = 30                                           ...(I)

Sum of the reciprocals of the numbers is $\frac{3}{20}$ mathematically it can be presented as,

$\frac{1}{p} +\frac{1}{q} =\frac{3}{20}$                                         ...(II)

From (II),

Making denominators alike by cross multiplying terms in left-hand side,

$\frac{p+q}{pq} =\frac{3}{20}$

$\frac{30}{pq} =\frac{3}{20}$                                             ...From(I)

⇒ $30*20 =3pq$

⇒ $\frac{30*20 }{3} =pq$

⇒ $pq=200$  

⇒ $p=\frac{200}{q}$                                             ...(III)

Substituting (III) in (I) we get,

$\frac{200}{q} +q=30$

⇒$200+q^2=30q$

Rearranging above as follows,

$q^2-30q+200=0$

Solving the above quadratic equation,

⇒$q^2-10q-20q+200=0$

⇒$q(q-10)-20(q-10)=0$

⇒$(q-10)(q-20)=0$

⇒q-10=0 or q=20=0

⇒q=10 or q=20

Hence,The required two numbers are 10 and 20.

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