General Questions
Practice and master this topic with our carefully crafted questions.
Let the number of boys and girls be x and y respectively. Then
From question, (x - y ) = 12% of (x + y)
⇒ x/y = 3/25 (x + y )
⇒ 25x - 25y = 3x + 3y
⇒ 22x = 28y
∴ x / y = 28 / 22 = 14 / 11
For dividing 12 into two whole numbers, the sum of the terms of the ratio must be a factor of 12. so, they cannot be in the ratio 3 :2.
If ₹ 782 be divided into three parts, proportional to 
: 
: 
, then the first part is:
Given ratio = : : = 6 : 8 : 9.
 1st part = ₹ |
 |
782 x | 6 |  |
= ₹ 204 |
| 23 |
Let the required number be N,
From question, (54 - N) / (71 - N) = (75 - N) / (99 - N)
⇒ (54 - N) x (99 - N) = (75 - N) x (71 - N)
⇒ N2 - 153N + 5346 = N2 - 146N + 5325
⇒ 7N = 21
∴ N = 3
Let 0.8 : 0.2 : : 0.2 : N
Then 0.8 x N = 0.2 x 0.2
∴ N = ( 0.2 x 0.2) / 0.8 = 0.04 / 0.08 = 4/80 = 0.05
Less length, less weight
From question, 13 : 6 : : 23.4 : W
⇒ 13 x W = 6 x 23.4
∴ W = (6 x 23.4) /13 = 10.8 kg
7 : 5 = 7/15 = 0.466
15 : 23 = 15/23 = 0.652
17 : 25 = 17/25 = 0.68
and 21 : 29 = 0.724
∴ The smallest one is 7 : 15.
Let the number be N,
From question, (6 + N) / (14 + N) = (18 + N) / (38 + N)
⇒ (6 + N) x (38 + N ) = (18 + N ) x (14 + N )
⇒ N2 + 44N + 228 = N2 + 32N + 252
⇒ 12N = 24
∴ N = 2
∵ (7 + N) / (13 + N) = 2/3
⇒ 3(7 +N) = 2(13 + N)
∴ N = 5
∵ 20 kg of brass contains zinc = 13 kg
∴ 100 kg of brass contains zinc = (13/20) x 100 kg. = 65 kg.