type 7 finding sum difference product based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (c)

Let the numbers be 7x and 11x respectively.

${7x + 7}/{11x + 7} = 2/3$

22x + 14 = 21x + 21

x = 7

Smaller number

= 7x = 7 × 7 = 49

Here, a = 7, b = 11, x = 7, c= 2, d = 3

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

= ${7 × 7(2 - 3)}/{7 × 3 - 11 × 2}$

= ${49 × -1}/{21 - 22}$ = 49

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

= ${7 × 11(2 - 3)}/{7 × 3 - 11 × 2}$

= ${77 × -1}/{21 - 22}$ = 77

Smallest number = 49

Answer: (a)

Let the numbers be 4x and 7x.

${4x + 4}/{7x + 4} = 3/5$

21x + 12 = 20x + 20

21x - 20x = 20 - 12

x = 8

Larger number

= 7x = 7 × 8 = 56

Using Rule 34,

a = 4, b = 7, c = 3,

d = 5, x = 4

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

= ${4 ×7(3 -5)}/{4 × 5 - 3 × 7}$

= ${4 × 7 × (-2)}/{20 - 21}$= 56

Answer: (b)

Using Rule 21,

Initially number of boys

= $8/{8 + 5} × 286 = 8/13 × 286$ = 176

Number of girls

= $5/13 × 286$ = 110

22 more girls get admitted.

∴ Required ratio

= $176/{110 + 22} = 176/132 = 4/3$ = 4 : 3

Answer: (c)

Let the numbers be 5x and 7x.

Now, ${5x - 9}/{7x - 9} = 7/11$

11 (5x - 9) = 7 (7x - 9)

55x - 99 = 49x - 63

55x - 49x = 99 - 63

6x = 36 ⇒ x = 6

Required difference

= 7x - 5x = 2x = 2 × 6 = 12

Here, a = 5, b = 7, x = 9, c = 7, d = 11

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

= ${9 ×5(11 - 7)}/{5 ×11 - 7 × 7}$

= ${45 × 4}/{55 - 49}$

= ${45 × 4}/6$= 30

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

= ${9 ×7(11 - 7)}/{5 ×11 - 7 × 7}$

= ${63 × 4}/{55 - 49}$

= ${63 × 4}/6$= 42

Their difference = 42 - 30 = 12

Answer: (b)

According to the question,

Sum of remaining two numbers

= 11 × 36 - 9 × 34

= 396 - 306 = 90

Ratio of the remaining two numbers = 2 : 3

Smaller number

= $2/5$ × 90 = 36