type 7 finding sum difference product based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Let the original number of students be 4x , 6x and 9x.

${4x + 12}/{6x +12} = 7/9$

42x + 84 = 36x + 108

42x - 36x = 108 - 84

6x = 24 ⇒ x = 4

Required number of students

= 19x = 19 × 4 = 76

Answer: (c)

Let the numbers be 3x and 5x.

${3x - 9}/{5x - 9} = 12/23$

69x - 60x = 207 - 108

$x =99/9$ 11

The smaller number = 3x = 33

Using Rule 35,

Here, a = 3, b = 5, x= 9, c = 12, d = 23

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

= ${9 ×3(23 - 12)}/{3 × 23 - 5 × 12}$

= ${27 × 11}/{69 - 60}$

=${27 × 11}/9$ = 33

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

= ${9 ×5(23 - 12)}/{3 × 23 - 5 × 12}$

= ${45 × 11}/{69 - 60}$

= ${45 × 11}/9$= 55

Smallest number = 33

Answer: (c)

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

According to the question,

$x^3 + (2x)^3 + (3x)^3$ = 4500

$x^3 + 8x^3 + 27x^3$ = 4500

$36x^3$ = 4500

$x^3 = 4500/36$ = 125

$x = √^3{125}$= 5 = smallest number

Answer: (a)

Let the numbers be $3/2$x and $8/3$x

According to question,

${3/2 x + 15}/{{8x}/3 + 15} = {5/3}/{5/2}$

${{3x + 30}/2}/{{8x + 45}/3} = 2/3$

${3(3x + 30)}/{2(8x + 45)} = 2/3$

${9x + 90}/{16x + 90} = 2/3$

27x + 270 = 32x + 180

32x - 27x = 270 - 180 = 90

5x = 90 ⇒ x = 18

The greater number

= $8/3 x = 8/3 × 18$ =48

Answer: (a)

Let the original number of boys and girls be x and y respectively.

Then $x/{y - 15} = 2/1$

x = 2y - 30 ....(i)

Again, ${x - 45}/{y - 15} =1/5$

5x - 225 = y - 15

5x = y - 15 + 225

5 (2y - 30) = y + 210

[From equation (i)]

10y - 150 = y + 210

10y - y = 210 + 150

9y = 360 ⇒ $y = 360/9$ = 40

Answer: (d)

Marks in English = 2x

Marks in Maths = 3x

Marks in Science = x

x + 2x + 3x = 180

6x = 180 ⇒ x = 30