First glass contains milk = 1/3 and water = 2/3
Second glass contains milk = 1/4 and water = 3/4
? Now tumbler contains water = (3/2 + 3/4) = 17/12
? Ratio of milk and water =7/12 : 17/12 =7 : 17
? A : B = 2 : 3, B : C = 2 : 3 and C:D = 2 : 3
? A : B = 8 : 12, B : C = 12 : 18 and C : D = 18 : 27
? A : B : C : D =8 : 12 : 18 : 27
So A's share = Rs. 1300 x ( 8 / 65) = Rs. 160
Milk = 60 x (2/3) litres =40 litres
Water = (60 - 40) litres = 20 litres
? 40 / (20 + x) = 1/2
? 20 + x = 80
? x = 60
Hence water to be added = 60 litres.
Let the numbers be 3x and 4x
Then, their L.C.M. = 12x
? 12x = 180
? x = 15
Hence, the first number = 45
Ratio of wages of 6 men, 8 women and 6 = (6 x 4) : (8 x 3) : (6 x 2) = 24: 24 : 12
= 2 : 2 : 1
? Total money earned by children = Rs. (950 x 1/5)
= Rs. 190
Let the numbers of hens = x and number of cows = y
Then x + y = 48 and 2x + 4y = 140
Solving these equations, we get 2y = 44
? y = 22
So, x = (48 - 22) = 26
? Number of hens = 26.
Let (a/b) = (c/d) = k
Then, a = bk and c = dk.
? (ma + nc) / (mb + nd) = (mbk + ndk) / (mb + nd) = k(mb + nd/mb + nd)
= k = a/b = a : b.
Let quantity of milk and water be 5x and x litres.
Then, 5x / (x + 5) = 5/2
? 10x = 5x + 25
? x =5
? Quantity of milk = 5x =25 litres
A : B = 4 : 5 = 8 : 10 and B : C = 2 : 3 = 10 : 15
? A : B : C = 8 : 10 :15
If A has Rs. 8, C has Rs. 15
If A has Rs. 800 C has Rs. (15/8 x 100) = Rs. 1500
Alcohol = (20/100) x 15 litres = 3 litres,
Water = 12 litres
New mix, contains,
Alcohol = 3 litres,
Water = 15 litres
? Percentage of alcohol in new mix. = (3/18) x 100 % = 162/ 3%
M = 3E and M/H = 4/3
? H = 3/4 M = 3/4 x 3E = 9/4 E
Now M + E + H = 250
? 3E + E + 9/4 E = 250
? 25 E = 1000
? E = 40
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