(01) Three glasses of equal volume contain acid mixed with water. The ratio of acid and water are 2: 3, 3: 4, and 4: 5 respectively, contents of these glasses are poured in large vessels. The ratio of acid and water in the large vessel is:
L.C.M. of 5, 7 and 9 is 315
Which is 5 x 63 = 7 x 45 = 9 x 35 = 315
Making Glass 1 = 126 : 189 = 315 (multiplying by 63)
Glass 2 = 135 : 180 = 315 (multiplying by 45)
Glass 3 = 140 : 175 = 315 (multiplying by 35)
Adding the ratios, we get 401 : 544
Ans. Thus the ratio of acid and water in the large vessel is 402: 544
(2) A vessel contains 60 litres of milk. 12 litres of milk is taken out from it and replaced by water. Then again from mixture, 12 litres are again taken out and replaced by water. The ratio of milk and water in the resultant mixture is:
Given: Vessel containes = 60 litres milk = c
Amount of milk replaced by water = 12 litres = x
Operations performed = 2 = n
Now, by using the formula, final quantity: initial quantity = [1 – x/c]n
= [1 – 12/ 60]2
= [4/5]2
= 16/ 25
Ans. Therefore ratio of milk and water in the resultant mixture is 16: 25.
(03) A can is full of a mixture of two liquids A and B in the ratio 7: 5. When 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid B, the ratio of A and B in the can becomes 7: 9. The capacity of the can is:
Given Initial Ratio = 7 : 5
Final ratio = 7 : 9
Drawn out liquid = 9 litres
To find: Capacity of can
Now, liquid A ratio is constant here, from initial to final ratio only liquid B is changing
Therefore, (9 – 5) = 4 units add
4 units = 9 litres
1 unit = 9/ 4 litres
12 unit = (9/ 4) x 12 = 27 litres
Initially solution = 27 + 9 = 36 litres
Quantity of liquid A initially = (7/(7 + 5)) x 36
= 21 litres
Ans. The capacity of the can is 21 litres
(04) Three containers whose volume are in the ratio 2: 3: 4 are full of mixture of spirit and water. In the first container the ratio of spirit and water is 4: 1. In second container the ratio is 11: 4 and in the third container ratio is 7: 3. All the three mixtures are mixed in a large container. The ratio of spirit and water in the resultant mixture is
Given:
volume ratio = 2: 3: 4
Ratio of first container = 4: 1
Ratio of second container = 11 :4
Ratio of third container = 7: 3
In 2 litres of first container,
Spirit = 2 × 4/ 5 = 8/ 5
Water = 2×1/ 5 = 2/ 5
In 3 litres of first container,
Spirit = 3 × 11/ 15 = 11/ 5
Water = 3 × 4/ 15 = 4/ 5
In 4 litres of first container,
Spirit = 4 × 7/ 10 = 14/ 5
Water = 4 × 3/ 10 = 6/ 5
therefore, Required ratio = (8/ 5 + 11/ 5 + 14/ 5) : (25 + 4/ 5 + 6/ 5)
= 33/ 5 : 12/ 5
= 33 : 12
= 11 : 4
Ans. Therefore required ratio is 11: 4
(05) Lala has lent some money to Arun at 5 % p.a. and Bhatia to 8 % p.a. At the end of the year, he has gained an overall interest of 6%. In what ratio has he lent the money to Arun and Bhatia?
