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

Answer: (b)

Average of two no's = 62

Sum of the numbers

= 62 × 2 = 124

Sum of the numbers = 124

If the larger number be x,

then smaller number = 124 - x

${124 - x + 2}/{x} =1/2$

252 - 2x = x

3x = 252 ⇒ x = 84

Smaller number

= 124 - 84 = 40

∴ Difference = 84 - 40 = 44

Answer: (a)

Let the numbers be x, y and z.

Then x : y = 2 : 3 ; y : z = 5 : 8

x : y : z = 2 × 5 : 3 × 5 : 3 × 8

= 10 : 15 : 24

Sum of the ratios

= 10 + 15 + 24 = 49

The second number

= $15/49$ × 98 = 30

Answer: (a)

Let the numbers be 3x, 2x and 5x respectively.

Now, $(3x)^2 + (2x)^2 + (5x)^2$ = 1862

$9x^2 + 4x^2 + 25x^2$ = 1862

$38x^2$ = 1862

$x^2 = 1862/38 = 49$

$x = √49 =7$

The smallest number

= 2x = 2 × 7 = 14

Answer: (d)

Numbers = 7x and 9x (let)

According to the question,

7x × 9x = 1575

$x^2 = 1575/{7 × 9}$ = 25

$x = √25$ = 5

Larger number = 9x

= 9 × 5 = 45

Answer: (a)

Let the numbers be 3x and 8x.

8x - 3x = 115

5x = 115

$x = 115/5$ = 23

The smaller number

= 3x = 3 × 23 = 69

Answer: (a)

Check through options

Number = 36

3 + 6 = 9; 6 - 3 = 3

and 36 : 9 = 4 : 1

Otherwise - 10x + y : x + y = 4 : 1

10x + (x + 3) : x + (x + 3) = 4 : 1

${11x + 3}/{2x + 3} = 4/1$

11x + 3 = 8x + 12

3x = 9

x = 3 and y = 6

Then the number is 36.