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

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: (c)

${6 + x}/{14 + x} ={18 +x}/{38 + x}$

From the given alternatives

${6 + 2}/{14 + 2} = {18 + 2}/{38 + 2}$

$1/2 = 1/2$

Using Rule 32,

Here, a = 6, b = 14, c = 18, d = 38

Required number x

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

= ${14 × 18 - 6 × 38}/{(6 + 38) - (14 + 18)}$

= ${252 - 228}/{44 - 32}$

= $24/12$ = 2

Answer: (b)

Ratio of numbers

= $1/2 : 2/3 : 3/4$

= $1/2 × 12 : 2/3 × 12 : 3/4 ×12$

= 6 : 8 : 9

Let the numbers be 6x, 8x and 9x.

Now, 9x - 6x = 36

x = 12

Numbers are 72, 96 and 108.

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