type 3 addition subtraction product on ratio & proportion Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

$(x + y)^2 = 4xy$

$x^2 + y^2 + 2xy - 4xy = 0$

$(x - y)^2$ = 0 ⇒ x = y

x : y = 1 : 1

Answer: (b)

Therefore, second number

=$9/{9 +16+4}×116$

=$9/29×116=36$

Answer: (d)

Let the nos. be 10x & 7 x then,

10 x - 7x = 105

3x = 105 ⇒ x = 35

Sum = 10x + 7x = 17x

= 17 × 35 = 595

Answer: (d)

Let the numbers be 3x and x,

Then, 3x + x = 240

4x = 240

$x = 240/4$ = 60

Difference = 3x - x = 2x

= 2 × 60 = 120

Answer: (c)

Let A = 4x and B = 5x.

According to the question,

$(5x)^2 - (4x)^2$ = 81

$25x^2 - 16x^2$ = 81

$9x^2 = 81 ⇒ x^2$ = 9

$x = √9$ = 3

A = 4x = 4 × 3 = 12

Answer: (b)

Let required number be x.

${6 +x}/{7 + x} = {15 + x}/{17 + x}$

$102 + 17x + 6x + x^2$

= $105 + 7x + 15x + x^2$

23x - 22x = 105 - 102

x = 3

Note : It is convenient to solve it orally using options

${6 + 3}/{7 + 3} = {15 + 3}/{17 + 3}$

= $9/10 = 18/20$

Required Number

= ${bc - ad}/{(a+d) - (b+c)}$

Where a = 6, b = 7, c = 15, d = 17

= ${7 × 15 - 6 × 17}/{(6 + 17) - (7 + 15)}$

= ${105 - 102}/{23 - 22}$ = 3