Answer: 9

Explanation:
Let the numbers of boys, girls and chocolates be B, G and C respectively. If each of student receives a chocolate, then one boy will have no chocolate. Hence, C = B + G -1. If two boys share one chocolate and the girls get one chocolate each, then the teacher is left with three chocolates.
Hence, C = B / 2 + G + 3
B / 2 + G + 3 = B + G – 1
B / 2 = 3 + 1
B = 8
Since B : G = 4 : 1, G = 2
C = 8 + 2 – 1 = 9

Answer: 16:15

Explanation:
Let 3 leaps of cat = 4 leaps of rat = k
One leap of cat = k/3 and one leap of rat = k/4
Cat takes 4 leaps for every 5 leaps of rat.
Distance traveled by cat / distance traveled by rat
4 ×k/3 / 5 × k/4
4/3 ÷ 5/4 = 16 / 15

Answer: 22.5

Explanation:
10 men + 6 boys complete the work in 20 days
(10 × 20) men + (6 × 20) boys complete the work in 1 day
200 men + 120 boys complete the work in 1 day => (1)
12 men + 4 boys complete the work in 18 days
(12 × 18) men + (4 × 18) boys complete the work in 1 day
216 men + 72 boys complete the work in 1 day => (2)
(216 – 200) men = (120 – 72) boys example. 16 men = 48boys
1 man = 3 boys.
10 men + 6 boys = 3 (10) boys + 6 boys = 36 boys
8 men + 8 boys = 3 (8) boys + 8 boys = 32 boys
36/32 = ?/20
? (36 × 20)/32 = 22.5 days

Answer: 15

Explanation:
 M/W = 5/1
Total Quantity = 60 litres
Milk = 5/6 × 60 = 50 litres
Water = 1/6 × 60 = 10 litres
Let x litres of water be added
50/10 + x = 2/1
30 = 2x => x = 15
15 litres of water should be added

Answer: 100

Explanation:
Let the parts be U, V, W, X
U + V + W + X = 1250 =>(1)
4U = 3V = 2W = X
U = X/4, V = X/3, W = X/2
Substituting in 1 we get,
(3X + 4X + 6X + 12X)/12 = 1250
25x/12 = 1250
x= 120 ×12 / 25 = 600
U = 600/4 = 150 ; V = 600/3 = 200; W = 600 / 2 = 300 and X = 600
300 - 200 = 100

Answer: 25

Explanation:
let the shares of A, B and C be A, B and C respectively.
It is given that, 9A = 6B = 3C
Dividing the above equations by 3, we have 3A = 2B = C
The ratio of A : B : C = 2 : 3 : 5.
Since the ratio is 2 : 3 : 6,
Let A = 2x, B = 3x and C = 6x.
2x + 3x+ 6x = 275
11x = 275
x = 25
B gets (3x – 2x = x) more than A, ie. Rs. 25 more than A

Answer: -193:293

Explanation:
x/y = 5/9
x2/y2 = 25/81
2/3(x2/y2) = 2/3(25/81) = 50/243
50 – 243/50 + 243
-193/293

Answer: 99

Explanation:
x α 1/y2 – 1, and x = K /y2 – 1, where K is the constant of proportionality.
Substituting the values of x and y in the above equation, (x = 24, y = 10), we have 24 = K / 100 – 1
K = 24 × 99 and x = (24 × 99) / y2 – 1 => (1)
To find the value of x, substitute y = 5 in the equation (1)
x = (24 × 99) / (25 – 1) = 99

Answer: Rs. 5200

Explanation:
it is given that the cost of the stone is directly proportional to cube of its weight.
Cost α W3
Cost = K × W3, where K is the constant of proportionality.
2500 = K × 103
K = 25000/1000 = 25
Since the wights of the stone are in the ratio of 1:1:3, weight of the largest stone = 3/5 × 10 = 6gm
And the weight of the smallest stone = 1/5 × 10 = 2gm
The difference in cost of the stones= K × 63 – K × 23
216K – 8K = 208K = 208 × 25
= Rs. 5200

Answer: 15 litres

Explanation:
Since the ratio of the water to alcohol is 2:1, let the amount of water and alcohol in the jar be 2x and x litres.
From the mixture, 6 litres of the mixture is replaced with water.
In this 6 litres, the amount of alcohol = 1/3 × 6 = 2 litres.
The amount of water = 2/3 × 6 = 4 litres
It is given that, (2x – 4 + 6) / x – 2 = 4/1
(2x + 2) / (x – 2) = 4/1
2x +2 = 4x – 8
2x = 10
c = 5
The capacity of the jar = 2x + x = 3x = 3 × 5 = 15 litres.