 Important for :
1
There are two numbers, 1st number is 12 more than the 2nd number. The average of the two numbers is 19. If 2 is added in both numbers, find the ratio of the numbers.
» Explain it
D
Let 1st number = x + 12, 2nd = x

Average = 19

 (x + x + 12) = 19 2

2x + 12 = 38

2x = 38 – 12

2x = 26

x = 13

1st = 25, 2nd = 13

Ratio = 25 + 2 : 13 + 2

= 27 : 15  = 9 : 5

Hence, option D is correct.

2
One-sixth of a number exceeds one-eighth of the same by 10. What is twice of the number?
» Explain it
B
Let the number be x.

 ∴ 1 x   – 1 x = 10 6 8

 ∴ 8x – 6x = 10 48

∴   2x = 480.

Hence, twice of the number is 480.

Hence, option B is correct.

3
There are 2 numbers in the ratio of 4 : 5. If 4 is subtracted from both numbers the ratio becomes 3 : 4. What will be the ratio if 4 is added in the both numbers?
» Explain it
C
Let the number = 4x,  5x

4x – 4 : 5x – 4 = 3 : 4

(4x – 4) × 4 = (5x – 4) × 3

16x – 16 = 15x – 12

16x – 15x = 16 – 12

x = 4

Numbers = 16, 20

Now Ratio = (16 + 4) : (20 + 4)

= 20 : 24 = 5 : 6

Hence, option C is correct.
4
Out of the three numbers, the ratio between the first and the second number is 5:6 and the ratio between the second and the third number is 15:16. If the difference between the first and the third number is 700, find the average of all the numbers.
» Explain it
A
1st : 2nd = 5:6

2nd : 3rd = 15:16

1st : 2nd : 3rd = 5 × 15 : 6 × 15 : 6 × 16

= 75 : 90 : 96

= 25 : 30 : 32

Difference between the first and the thirst number = 700

32x - 25x = 700

7x = 700

x = 100

Number, 1st = 25 × 100 = 2500, 2nd = 30 × 100 = 3000, 32 × 100 = 3200

 Average = 2500 + 3000 + 3200 3

 = 8700 = 2900 3

Hence, option A is correct.