1. A 10 Liter mixture of milk and water contains 30 percent water. Two liters of this mixture is taken away. How many liters of water should now be added so that the amount of milk in the mixture is double that of water?
Two liters were taken away So we have only 8 liters of mixture.
Amount of milk in 8 liters of mixture = 8 × 70% = 5.6 liters
Amount of water in 8 lit of mix = 8 - 5.6 = 2.4 liters.
Half of milk i.e half of 5.6 = 2.8 liters.
We need (2.8 - 2.4) liters water more = 0.4 lit
2. A frog can climb up a well at 3 ft per min but due to slipperiness of the well, frog slips down 2 ft before it starts climbing the next minute. If the depth of the well is 57 ft, how much time will the frog take to reach the top?
Answer: 55 min
As per given, in 1 min,frog climbs up 3 ft and slips down by 2 ft.
So the frog climbs only 1 ft in 1 min
So after 54 mins,it would have climbed 54ft.
At the end of 55 mins it climbs up 3 ft to make it 57 ft and come out of the well.
Once it had reached the destination,it will not slip.
So the frog will take only 55 minutes to climb up the well.
3. A rectangle has twice the area of a square. The length of the rectangle is 14 cm greater than that side of the square whereas breadth is equal to side of the square. Find the perimeter of the square?
(a) 42 cm
(b) 14 cm
(c) 56 cm
(d) 28 cm
Let side of square be x.
Then for rectangle length = 14 + x and breadth = x.
It is given
Area of rectangle = 2 × (area of square)
length × breadth = 2(x × x)
(x + 14) × x = 2 × x2
x2 + 14x = 2x2
x2 = 14x
x = 14.
Perimeter of square = 4 × x = 56
4. A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
(a) 5 hrs
(b) 4 hrs
(c) 12 hrs
(d) 6 hrs
He covered 5 km in 1 hour , so he might cover 20 km in 4 hours.
But he took 10 hours.
He would have saved 10 – 4 = 6 hours.
5.If half of 5 were 3, that would one-third of 10 be
Half of 5 is 2.5. But given as 3. So take 1/2 of 5x = 3 ⇒ x = 6/5
Now 1/3 (10x) = 1/3 × 10 × 6/5 = 4.