1. A stream, which flows at a uniform rate of 2.5 km per hour, is 20 metres wide. If the depth of a certain ferry is 1.2 m, how many litres of water will pass through the ferry in a minute?
A) 1000000
B) 900000
C) 500000
D) None of these
Ans. A
The total quantity of water =
=
= 1000 m3 = 1000000 litres
2. The annual rainfall at a place is 43 cm. Find the weight (in metric tonnes) of the annual
rainfall on a hectare of land, taking the weight of water to be 1 metric tonne for 1 cubic metre.
A) 4000
B) 4300
C) 5000
D) None of these
Ans. B
Height of water on 1 sq m area of land annually = 43 cm
Volume of water on 10,000 sq m. area of land = × 10000 m3 = 4300 m3
Weight of water = 4300 metric ton
3. A metallic right circular cone of height 9 cm and base radius 7 cm is melted into a cuboid with two sides as 11 cm and 6 cm. What is the third side of the cuboid?
A) 5 cm
B) 6 cm
C) 7 cm
D) 9 cm
Ans. C
Let the third side of cuboid = x cm
Now, according to the question:
1/3 πr2h = l × b × h
⇒ 66x = 462
⇒ x = 7 cm
4. A garden is 112m long & 78 m wide. It has walking path 25m wide all around it on inside. Find the area of path ?
A) 925 m2
B) 927 m2
C) 929 m2
D) 934 m2
Ans. A
If path is within the garden then use this formula:
2 * B * (L + B – 2 * B)
2 * 25 (112 + 78 – 2 * 25)
= 5 * 185 = 925 m2
5. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs100 per metre it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?
A) 274 & 100 m
B) 275 & 200 m
C) 275 & 100 m
D) None of the above
Ans. C
Let the common ratio between the length and breadth of the rectangular plot be x. Hence, the length and breadth of the rectangular plot will be 11x m and 4x m respectively.
Perimeter of the plot = 2(Length + Breadth)
It is given that the cost of fencing the plot at the rate of Rs 100 per metre is Rs 75, 000.
∴ 100 × Perimeter = 75000
100 × 30x = 75000
3000x = 75000
Dividing both sides by 3000, we obtain
x = 25
Length = 11x m = (11 × 25) m = 275 m
Breadth = 4x m = (4 × 25) m = 100 m
Hence, the dimensions of the plot are 275 m and 100 m respectively.
