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Application sums
1) Renu leaving his house at 8 am and he decided filled the petrol in bunk on the way to his office. He travelled at 75% of his regular speed and he reached the petrol bunk in 20 minutes. If he takes 30 minutes to reach the office in regular days, then the distance between house and petrol bunk is what percent of the distance between house and office?
A) 20%
B) 40%
C) 30%
D) 50%
E) 60%
2) If the tank connected with 4 pipes some of them are filled the tank and some of them are emptied the tank. Each of the inlet pipes can fill the tank in 2 hours while each outlet pipes can empty the tank in 1.5 hours. If all the pipes are opened and the tank full, how many pipes are empty the tank?
A) 2
B) 3
C) 1
D) Cannot be determine
E) None of these
3) If the perimeter of the square is 48 cm and the ratio of the length to breadth of the rectangle is 3: 2. If the side of the square is 2 cm less than the breadth of the rectangle and the circumference of the circle is 18 cm more than the perimeter of the rectangle, then what is the difference between the area of the rectangle and circle?
A) 326 cm2
B) 324 cm2
C) 322 cm2
D) 320 cm2
E) None of these
4) A vessel contains milk and water, in which 45 % is water. 60 litres of mixture was taken out and replaced with 69 litres of water and the ratio becomes 7: 12. Find the initial quantity of milk in the vessel?
A) 99 litres
B) 88 litres
C) 55 litres
D) 110 litres
E) None of these
5) The average age of 8 (A to H) persons in the class is 40 years. If the average age of A, B and C is 32 years, the average age of F, G and H is 4 years more than the average ages of A, B and C and the D’s age is 16 years less than E. Find the age of E?
A) 66 years
B) 72 years
C) 70 years
D) 68 years
E) None of these
6) A box contains two blue, five red and three yellow balls. Three balls are drawn randomly. What is the probability that exactly one of them is blue?
A) 53/120
B) 9/20
C) 47/120
D) 49/120
E) None of these
7) Average age of Renu, Ram and Rani is 10 years more than the average age of Renu, Rani and Richie. If the average age of all of them is 57 years and the average age of Renu and Rani is 16 years, then what is the ratio of Ram to Richie after 10 years?
A) 43: 33
B) 21: 16
C) 41: 31
D) 20: 15
E) None of these
8) If Rahul invests 25% of his amount in scheme A which offers simple interest at the rate of 15% per annum, 30% of his amount in scheme B which offers simple interest at the rate of 12% per annum and remaining amount in scheme C which offers simple interest at rate of 20% per annum. If after 4 years he received the total amount Rs.13232, then find amount invests in scheme B?
A) Rs.2100
B) Rs.2400
C) Rs.2700
D) Rs.3000
E) None of these
9) The ratio of the speed of boat A to speed of stream is 3: 2 and the ratio of the speed of boat B to speed of stream is 7: 5. If the difference between the speed of boat A and boat B is 2 kmph, then what is the difference between time taken by boat A covers 150 km along with stream and the time taken by boat B covers 120 km against stream?
A) 10 hours
B) 12 hours
C) 16 hours
D) 14 hours
E) None of these
10) The train crosses a 400 m long platform and pole is 24 seconds and 12 seconds respectively. The train crosses a man running in opposite direction in 9 seconds. What is the speed of man?
A) 40 kmph
B) 50 kmph
C) 60 kmph
D) 30 kmph
E) None of these
Answers :
Directions (1-10) :
1) Answer: D
Distance = speed * time
Let the original speed be 100x
Then Decreased speed = 100x * 75/100 = 75x
Distance between house and petrol bunk = 20 * 75x = 1500x
Distance between House and Office = 30 * 100x = 3000x
Required % = (1500x/3000x) * 100 = 50%
2) Answer: D
Number of inlet pipes = x
Number of emptied pipes = 4 – x
((4 – x)/1.5) – (x/2) = 1/y
The tank completely filled or emptied time is not given.
3) Answer: C
Side of the square = 48/4 = 12 cm
Breadth of the rectangle = 12 + 2 = 14 cm
Length of the rectangle = 14 * 3/2 = 21 cm
Perimeter of the rectangle = 2 * (21 + 14) = 70 cm
Circumference of the circle = 70 + 18 = 88 cm
2 * 22/7 * r = 88
Radius of the circle = 14 cm
Area of the rectangle = 21 * 14 =294 cm2
Area of the circle = 22/7 * 14 * 14 = 616 cm2
Difference = 616 – 294 = 322 cm2
4) Answer: D
The ratio of milk and water = 55 : 45 = 11 : 9
The quantity of milk taken out = 60 * (11/20) = 33 litres
The quantity of milk taken out = 60 * (9/20) = 27 litres
Given,
(11x – 33) / (9x – 27 + 69) = (7/12)
132x – 396 = 63x + 294
69x = 690
x = 10
The initial quantity of milk in the vessel = 11x = 110 litres
5) Answer: A
A + B + C + D + E + F + G + H = 40 * 8 = 320 years
A + B + C = 32 * 3 = 96 years
F + G + H = (32 + 4) * 3 = 108 years
E – D = 16 ———- (1)
E + D = 320 – 96 – 108 = 116 ——— (2)
(2) + (1)
2E = 116 + 16 = 132
E = 66 years
6) Answer: E
Required Probability = (2C1Â * 5C1Â * 3C1/10C3) + (2C1* 5C2/10C3) + (2C1* 3C2/10C3)
= 30/120 + 20/120 + 6/120
= 56/120 = 7/15
7) Answer: C
Renu + Ram + Rani + Richie = 57 * 4 = 228 years
(Renu + Rani + Ram)/3 – (Renu + Rani + Richie)/3 = 10
Ram – Richie = 30 ————- (1)
Renu + Rani = 16 * 2 = 32 years
Ram + Richie = 228 – 32 = 196 ———- (2)
(2) + (1)
2Ram = 226
Ram = 113
After 10 years Ram = 113 + 10 = 123
Richie = 113 – 30 = 83
After 10 years = 83 + 10 = 93 years
Required ratio = 123: 93
= 41: 31
8) Answer: B
Rahul = x
SI = P * N * R/100
(25/100 * x * 15 * 4/100) + (30/100 * x * 12 * 4/100) + (45/100 * x * 20 * 4/100) = 13232 – x
15x/100 + 144x/1000 + 36x/100 = 13232 – x
654x = 13232000 – 1000x
x = Rs.8000
Amount invest in scheme B = 8000 * 30/100 = Rs.2400
9) Answer: B
Ratio of speed of boat A, stream and boat B = 15: 10: 14
15x – 14x = 2 kmph
x = 2 kmph
Speed of boat A = 15 * 2 = 30 kmph
Speed of boat B = 14 * 2 = 28 kmph
Speed of stream = 10 * 2 = 20 kmph
Required difference = 120/(28 – 20) – (150/(30 + 20))
= 15 – 3 = 12 hours
10) Answer: A
Length of train = x
Speed of train = y
Speed of man = z
x + 400 = y * 5/18 * 24
3x + 1200 = 20y
x = y * 5/18 * 12
3x = 10y
10y + 1200 = 20y
10y = 1200
y = 120 kmph
x = 1200/3
x = 400 m
400 = (120 + z) * 5/18 * 9
800 = 600 + 5z
5z = 200
z = 40 kmph
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