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

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: (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: (b)

Let the two numbers are x and y.

According to the question,

$x/y = 5/7$

7x = 5y

7x - 5y = 0 ...(I)

Again, ${x - 40}/{y - 40} =17/27$

27x - 1080 = 17y - 680

27x - 17y = 1080 - 680

27x - 17y = 400 ...(II)

From (I) × 17 - (II) × 5, we have

-16x = -2000

x = 125

Putting the value of x in equation (I)

7 × 125 = 5y

$y = {7 × 125}/5$ = 175

Difference of the numbers

= 175 - 125 = 50

Here, a = 5, b = 7, x = 40

c = 17, d = 27

The two numbers are

= ${xa(d-c)}/{ad-bc}$

= ${40 ×5(27 - 17)}/{5 × 27 - 7 × 17}$

= ${200 × 10}/{135 - 119}$

= $2000/16 = 500/4$

1st Number = 125

And = ${xb(d-c)}/{ad-bc}$

= ${40 ×7(27 - 17)}/{5 × 27 - 7 × 17}$

= ${280 × 10}/{135 - 119}$

= $2800/16 = 700/4$

2nd Number = 175

Their difference= 175 - 125 = 50

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