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

Answer: (a)

Original number of boys in school

= $5/9$ × 432 = 240

Number of girls

= 432 - 240 = 192

Let the new number of girls be x.

According to the question,

${240 + 12}/{192 + x} = 7/6$

$252/{192 + x} = 7/6$

192 × 7 + 7x = 252 × 6

1344 + 7x = 1512

7x = 1512 - 1344 = 168

$x = 168/7$ = 24

Answer: (a)

Let the numbers be 3x and 5x.

${3x + 10}/{5x + 10} = 5/7$

25x + 50 = 21x + 70

4x = 20 ⇒ x = 5

Smaller number

= 3x = 3 × 5 = 15

Using Rule 34,

Here, a = 3, b = 5, c = 5, d = 7, x = 10

Smallest number = ${xa(c-d)}/{ad-bc}$ a < b

= ${10 × 3(5 - 7)}/{3 × 7 - 5 × 5}$

= ${- 60}/{21 - 25} = 60/4$ = 15

Answer: (d)

Let the original number of students be 2x, 3x and 4x in three class.

According to the question,

${2x + 12}/{3x + 12} = 8/11$

24x + 96 = 22x + 132

2x = 132 - 96 = 36

$x = 36/2$ = 18

Original number of students

= 2x + 3x + 4x

= 9x = 9 × 18 = 162

Answer: (a)

Let the numbers be x and 5x.

According to the question,

x × 5x = 320

$5x^2$ = 320

$x^2 = 320/5$ = 64

$x = √64$ = 8

Required difference

= $(5x)^2 - x^2$

= $25x^2 - x^2 = 24x^2$

= 24 × 8 × 8 = 1536

Answer: (c)

Required number = x

${11 - x}/{15 - x} = 2/3$

33 - 3x = 30 - 2x

3x - 2x = 33 - 30

x = 3

Answer: (a)

According to the question,

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

(Numbers = 3x and 5x )

69x - 207 = 60x - 108

9x = 207 - 108 = 99

x = 11

Required numbers

3 × 11 = 33 and 5 × 11 = 55

Using Rule 35,

Here, a = 3, b = 5, c = 12,

d = 23, x = 9

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

Numbers are 33, 55