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

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: (d)

Ratio of numbers = 2 : 3

Sum of ratios = 2 + 3 = 5

First number = $2/5 × 125$ = 50

Second number = $3/5 × 125$ = 75

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: (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

Answer: (b)

According to the question,

The number 84 must be a multiple of sum of the terms of ratio.

For ratio 3 : 2,

Sum of the terms of ratio

= 3 + 2 = 5

which is not a factor of 84.

Answer: (d)

Let three numbers be a, b and c respectively.

According to the question,

a + b + c = 540

and b : c = 9 : 13

a : c = 2 : 7

$a/c × c/b = 2/7 × 13/9$

$a/b = 26/63$

b : c = 9 : 13 = 63 : 91

a : b : c = 26 : 63 : 91

Sum of the terms of ratio

= 26 + 63 + 91 = 180

c = $91/180 × 540$ = 273