Question

42. The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. The numbers are :
(a) 12,5
(b) 13, 4
(c) 14,3
(d) 24, 10
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Answer 1

Answer:

I hope it is correct, and this will help u...

Step-by-step explanation:

Let the positive integers are x and y where x > y.

As per the first statement

x (x+y) = 204

=> x^2 + xy = 204 ………..Eq 1

As per the second statement

y (x-y) = 35

=> xy - y^2 = 35 ………..Eq 2

Subtracting Eq2 from Eq1, we will get

x^2 +xy - (xy - y^2) = 204 - 35

=> x^2 + xy - xy + y^2 = 169

=> x^2 + y^2 = 169

=> x^2 + y^2 = 13^2

According to Pythagoras theorem,

Sum of square of Height and Base = to square of Hypotenues.

=> x^2 + y^2 = 13^2

Using hit and trial method we will get the value of x and y

ie. 12^2 + 5^2 = 13^2

=> 144 + 25 = 169

=> 169 = 169

So x = 12 and y = 5

Ans: 12 and 5

Answer 2

SOLUTION :-

Let,

Bigger number = x

Smaller number = y

According to the first condition,

$\longrightarrow\quad \sf x(x+y)=204 \\\\\longrightarrow\quad x^2+xy= 204 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition,

$\longrightarrow\quad \sf y(x-y)=35\\\\\longrightarrow\quad xy-y^2=35\\\\\longrightarrow\quad y^2-xy=-35 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(2)$

Equation (2) + Equation (1)

$\longrightarrow\quad\sf x^2+y^2=169\\\\\longrightarrow\quad x^2+y^2= 13^2$

We know that 12, 5 and 13 are Pythagoras triplets.

$\therefore \bf x = 12 \ , \ y = 5$

The numbers are 12 and 5.

Option (a) is correct.