type 3 addition subtraction product on ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

Let the numbers be 3x and 4x.

${3x + 6}/{4x + 6} = 4/5$

16x + 24 = 15x + 30

x = 30 - 24 = 6

Required difference = 6

Here, a = 3, b= 4, x = 6

c = 4, d = 5

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

= ${6.3(4 - 5)}/{3 ×5 - 4 × 4}$

= ${18 × -1}/{15 - 16}$ = 18

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

= ${6 × 4(4 - 5)}/{3 × 5 - 4 × 4}$

= ${24 × (-1)}/{15 - 16}$ = 24

Numbers are 24 and 18.

Their difference = 24 - 18 = 6

Answer: (a)

x + y = 3 (x - y)

x + y = 3x - 3y

2x = 4y

$x/y = 2/1$

x : y = 2 : 1

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: (d)

Numbers = 5x and 8x

According to the question,

8x - 5x = 48

3x = 48 ⇒ x = 16

Smaller number = 5x

= 5 × 16 = 80

Answer: (d)

A : B = 8 : 9

B : C = 3 : 4 = 9 : 12

A : B : C = 8 : 9 : 12

Numbers = 8x, 9x and 12x

8x × 12x = 2400

$x^2 = 2400/{8 × 12} = 25$

$x = √25$ = 5

A + B + C

= 8x + 9x + 12x = 29x

= 29 × 5 = 145