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

Answer: (a)

From the given options number = 5, because

${7 + 5}/{16 + 5} = {43 + 5}/{79 + 5}$

$12/21 = 48/84$

[check other options likewise]

Using Rule 32,

Here, a = 7, b=16, c = 43, d= 79

Required number

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

= ${16 × 43 - 7 × 79}/{(7 + 79) - (16 + 43)}$

= ${688 - 553}/{86 - 79}$

= $35/7$ = 5

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

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: (c)

Number of balls in bag x and y respectively

= 2a and 3a

3a - 5 = 2a + 3

a = 5 + 3 = 8

Total number of balls

= 5a = 40

Balls in each bag = 20

Answer: (c)

Let the integers be 9x and 7x respectively.

According to the question,

9x × 7x = 1575

$x^2 = 1575/63$

$x^2 = 25 ⇒ x = 5

[x being positive (+ve) integer]

Smaller integer

= 7x = 7 × 5 = 35

Answer: (a)

Numbers = 2x, 3x and 5x,

According to question,

$(2x)^2 + (3x)^2 + (5x)^2$ = 608

$4x^2 + 9x^2 + 25x^2$ = 608

$38x^2$ = 608

$x^2 = 608/38$ = 16

$x = √16$ = 4

Numbers ⇒ 2x = 2 × 4 = 8

3x = 3 × 4 = 12

5x = 5 × 4 = 20