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

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

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: (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: (a)

Let the number to be subtracted be x.

According to the question,

${7 - x}/{9 - x} ={11 - x}/{15 - x}$

Now, check through options

Clearly, putting x = 3,

Each ratio = $2/3$.

Note : Solve such questions orally by mental exercise.

The number will be x

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

= ${7 × 15 - 9 × 11}/{(7 + 15) - (9 + 11)}$

= ${105 - 99}/{22 - 20} = 6/2$ = 3

Answer: (d)

Let the numbers be a, b and c.

Now, a : b = 8 : 9

b : c = 3 : 4

a : b : c

= 8 × 3 : 9 × 3 : 9 × 4

= 24 : 27 : 36 = 8 : 9 : 12

$a/8 = b/9 = c/12= k$

a = 8k, b = 9k, c = 12k

According to the question,

8k × 12k = 2400

$k^2 = 2400/{8 × 12}$ = 25

k = 5

Second number

= 9k = 9 × 5 = 45

Answer: (d)

Let the number be 2x and 3x.

Then. ${2x -2}/{3x + 2} = 1/2$

4x - 4 = 3x + 2

x = 6

Sum of numbers = 5x

= 5 × 6 = 30