Q1. A cylindrical flask, whose circular part has a diameter of 35 cm is filled with water up to a height of 24 cm. A solid iron spherical ball of radius 12 cm is dropped in the flask to submerge completely in water. Find the increase in the level of water (in cm) (rounded off to two decimal places).
(a) 8.56
(b) 8.24
(c) 7.88
(d) 7.52
Q2. The difference between the outside and inside surface area of a hollow spherical metallic ball having outer diameter of 35 cm, is 2464 cm^2. Find the volume of the inner part of the sphere(in cm^3) .
(a) 539
(b) 4851
(c) 639/5
(d) 255
Q3. Marked price of two articles is Rs.2800 each. One is sold at a discount of 24% and the other for Rs. 1200 more than the marked price. If the net profit is 25%. Find the total cost price of articles.
(a) Rs. 4,500.5
(b) Rs. 4,902.4
(c) Rs. 4,800
(d) Rs. 4,600.25
Q4. Profit on selling 12 oranges equals sellings price of 4 apples. While loss on sellings 12 apples equals selling price of 6 oranges. Also profit percentage equals to the loss percentage and cost of an orange is one third of the cost of an apple. What is the ratio of selling price of orange to the sellings price of an apple?
(a) 5 : 4
(b) 2 : 1
(c) 4 : 5
(d) 3 : 4
Q5. Train A, travelling at 90 kmph, overtook train B, traveling in the same direction, in 5 seconds. If train B had been traveling at twice its speed, then train A would have taken 15 seconds to overtake it. Find the length of train B, given that it is half the length of train A.
(a) 25 m
(b) 50 m
(c) 75 m
(d) 150 m
Q6.Samartha is five times as old as his daughter Trisha and Samartha’s wife Phalguni’s age is 26 years more than that of Trisha. The difference between thrice the age of Samarth ten years ago and twice the age of Phalguni ten years ago was 42 years. What will be the respective ratio of Phalguni’s age 12 years hence and Samartha’s age 2 years hence ?
(a) 23 : 21
(b) 24 : 29
(c) 19 : 23
(d) 21 : 25
Q7. Abhay and Anushka started a business and invested Rs. 12,500 and Rs. 20,000 respectively. At the end of year they decided to distribute 50% of profit equally among them and remaining in capital ratio. Had they distributed entire profit in capital ratio, Abhay got Rs. 3,78 less. Find the total profit amount.
(a) Rs. 6,000
(b) Rs. 6,552
(c) Rs. 5500
(d) Rs. 5650
Q8. Several litres of alcohol drawn off a 72 litre vessel full of alcohol and equal amount of water added. Again, the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 18 litres of pure alcohol. How much the alcohol was drawn off initially?
(a) 30 litres
(b) 37 litres
(c) 39 litres
(d) 36 litres
Q9. The simple interest on a sum of money will be Rs. 450 after five years. In the next seven years principal becomes six times, what will be the total interest at the end of 12th year?
(a) Rs. 1200
(b) Rs. 1080
(c) Rs. 1100
(d) Rs. 1000
Q10. An inlet pipe can fill a tank in 8 hours and an outlet can empty the same tank in 40 hours, working individually. How many minimum additional number of outlet pipes of the same capacity are required to be opened, so that the tank never overflows?
(a) 6
(b) 5
(c) 8
(d) 7
Solutions:
S1. Ans.(d)
Sol.
Let level of water will be increased by h.
π×(35/2)^2×h=4/3 π(12)^3
⇒h=4/3×(12×12×12×4)/(35×35)
=7.52 cm
S3. Ans.(b)
Sol. Let total cost price of articles = 100 x
∴ 2800×76/100+2800+1200=125/100×100x
x = Rs.49.024
cost price = Rs.4902.4
S5. Ans.(a)
Sol.
Let length of train B = x m
∴ length of train A = 2x m
Let speed of train B = s m/sec
And, speed of train A(in m/sec)
=90×5/18
= 25 m/sec
ATQ,
(25 – s) × 5 = (25 – 2s) ×15
⇒ 25 – s = 75 – 6s
⇒ s = 10 m/sec
∴ Length of train B
=((25-10)×5)/3
= 25 m
S6. Ans.(a)
Sol.
Let Trisha’s age = x
∴ Samartha’s age = 5x
Phalguni’s age = x + 26
ATQ,
⇒ 3(5x – 10) – 2 (x + 26 – 10) = 42
⇒ x = 8
∴ Required ratio=(8+26+12)/(5×8+2)
=46/42
=23/21
S7. Ans.(b)
Sol. Ratio of their investments = 12500:20000
= 5:8
Let x be the total profit amount, then
ATQ, (x/4+5/13×x/2)-(5/13×x)=378
Or, (13x-10x)/52=378
Or, x= Rs. 6552
S9. Ans.(b)
Sol. Simple interest on sum after 5 years = 450
Simple Interest for 1 year = 90
Simple Interest for 12 year = 90 × 12 = 1080
