11. How many kilograms of rice of Rs.5.4 per kg should be mixed with 10 kg of rice of Rs.4.5 per kg, such that there may be the gain of 20% by selling the mixture at Rs.5.94 per kg?
A. 10 kg B. 12 kg C. 15 kg D. 8 kg
Answer: A
Let the quantity of Rs.5.4 per kg rice = x kg
According to the question,
x × 5.4 + 4.5 × 10 = 5.94 × (10 + x) ÷ 120 × 100
5.4x + 45 = 4.95 × (10 + x)
5.4x + 45 = 49.5 + 4.95x
5.4x – 4.95x = 49.5 – 45
0.45x = 4.5
x = 10 kg
12. In the Mumbai Zoo, there are some ducks and some rabbits. If the heads counted there are 160, while the legs are 450. What will be the number of Rabbits in the zoo?
A. 65 B. 60 C. 95 D. 85 E. 100
Answer: A
Let, Ducks = x, Rabbit = y
As, Duck has 2 legs and rabbit has 4 legs,
Both have one head,
2x + 4y = 450 …1
x + y = 160
2x + 2y = 320 …. 2
Equation 1 – Equation 2
2y = 130
y = 65
13. The ratio of milk to water in three containers of equal capacity is 3 : 2, 7 : 3 and 11 : 4 respectively. The three containers are mixed together. What is the ratio of milk to water after mixing?
A. 21 : 9 B. 41 : 18 C. 61 : 29 D. 38 : 8
Answer: C
Let the capacity of each be ‘a’ litre
Then quantity of milk in the container after mixing is
((3/5) + (7/10) + (11/15) )a
= ( (3 × 6 + 7 × 3 + 11 × 2) / 30 )a
= (61/30)a
And quantity of water in container after mixing is
((2/5) + (3/10) + (4/15) )a
= (29/30)a
⇒ required ratio of milk to water after mixing
= (61/30)a / (29/ 30)a = 61:29
14. The amount of water (in ml) that should be added to reduce 7 ml lotion, containing 70% alcohol, to a lotion containing 35% alcohol, is
A. 35 ml B. 4 ml C. 7 ml D. 10.5 ml
Answer: C
Let the required volume of water to be added = x ml
When added to 7 ml lotion, the total volume = “7 + x” ml
If the lotion contains 70% alcohol, then it contains 30% water
If it contains 35% alcohol, it contains 65% water.
By balancing the volume of water before and after dilution of the lotion, we get :
(Amount of water in lotion before dilution) + (amount of water added) = (amount of water in lotion after
dilution)
(30% of 7) + x = (65% of “7 + x”)
⇒(30 × (7/100) ) + x = 65 × ((7 + x)/100)
⇒ 210 + 100x = 65 × (7 + x)
⇒ 210 + 100x = 455 + 65x
⇒ 35x = 245
⇒ x = 7
15. How many litres of water should be added to a 35-litre mixture of milk and water containing milk and water in the ratio of 4 : 3 such that the resultant mixture has 60% water in it?
A. 12 B. 10 C. 21 D. 15
Answer: D
The quantity of milk in the mixture
= 35 × (4/7) = 20 litres
The quantity of water in the mixture = 35 – 20 = 15 litres
Now, let the quantity of water added to the mixture be x litres. Then water becomes 60% of the total quantity
of mixture.
∴ Required % of water in mixture
= Total quantity of water / Total quantity of mixture = 60%
(15 + x ) / (35 + x )= 3/5
⇒ 75 + 5x = 105 + 3x
⇒ 2x = 30
∴ x = 15 litres.
