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

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

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: (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)

Numbers = 5x and 8x

According to the question,

8x - 5x = 48

3x = 48 ⇒ x = 16

Smaller number = 5x

= 5 × 16 = 80

Answer: (a)

Let the numbers be 2x and 3x respectively.

According to the question,

${2x + 8}/{3x + 8}= 3/4$

9x + 24 = 8x + 32

9x - 8x = 32 - 24 = 8

x = 8

Sum of numbers

= 2x + 3x = 5x

= 5 × 8 = 40

Here, a = 2, b = 3, x= 8,

c = 3, d = 4

1st Number = ${xa(c-d)}/{ad-bc}$

= ${8 × 2(3 - 4)}/{2 × 4 - 3 × 3}$

= ${- 16}/{- 1}$ = 16

2nd Number = ${xb(c-d)}/{ad-bc}$

= ${8 × 3(3 - 4)}/{2 × 4 - 3 × 3}$

= ${- 24}/{- 1}$ = 24

Sum of numbers = 16 + 24 = 40

Answer: (a)

x + y = 3 (x - y)

x + y = 3x - 3y

2x = 4y

$x/y = 2/1$

x : y = 2 : 1