1. The respective ratio between the speeds of a car and a jeep is 3 : 5. The speed of the jeep is 250 percent of the speed of the tractor which covers 570 km in 19 hours. What is the average speed of car and jeep together?

Ans:1
Speed of tractor = 570/19 = 30 km/h
Speed of jeep = 30 x 2.5 = 75 km/h
Speed of car = 3/5 x 75 = 45 km/h
Required avg speed = (75+45)/2 = 60 km/h

2. The percentage profit earned by selling an article for Rs. 1600 is equal to the percentage loss by selling the same article for Rs. 1100. At what price should the article be sold to make 20% profit?

Ans:4
Let the C.P. be Rs. x.
Then, 100 (1600 – x)/x = 100 (x – 1100)/x
=> 2x = 2700
=> x = 1350
∴ Required S.P. = 120% of Rs. 1350 = Rs. (120/100) X 1350 = Rs. 1620

3. Amar and Prem start a business with initial investments in the ratio of 14:6. Their profits are in the ratio of 8:3 at the end of the year. If Amar invested his money for 8 months, find the time for which Prem invested his money.

Ans:5
Suppose Prem invested his money for N months.
Ratio of profits = (14 x 8)/(6 x N)= 8/3
N = 7 months

4. A man can row three quarters of a kilometer against the stream in (15/2) minutes and return in (45/8) minutes. The speed of the man in still water is

Ans: 5
Three quarters of a kilometer means ¾ distance
Upstream speed= (3/4)/ (15/(2*60))=(3/4)*(120/15)=6kmph
Downstream speed= (3/4)/ (45/(8*60))=(3/4)*(480/45)=8kmph
Hence, speed in still water= (6+8)/2=7kmph

5. Ramesh and Suresh are running around a circular field whose circumference is 200 meter. Speeds of Ramesh and Suresh are 5 m/sec and 8 m/sec. If both start running from the same point in the same direction, how many times will they meet in 1 hour?

Ans: 3
Time taken by Ramesh to complete 1 round = 200/5 = 40 seconds
Time taken by Suresh to complete 1 round = 200/8 = 25 seconds
Number of rounds completed by Ramesh in 1 hour = (60 X 60)/40 = 90 rounds
Number of rounds completed by Suresh in 1 hour = (60 X 60)/25 = 144 rounds
Since they are running in the same direction, number of times they would have met = 144 – 90 = 54

6. The largest and the second largest angles of a triangle are in the ratio of 4:3 respectively. The numeric value of the smallest angle of the triangle is three less than the square of six. What is the value of the largest angle of the triangle?

Ans:3
Smallest angle = 36-3 = 33
Let the other two angles be 4x, 3x.
7x+33= 180
=> x = 21
Largest angle = 21×4=84

7. What is the volume of the cone whose radius is two times the side of the cube of volume 729 units and whose height is double the side of the cube having a volume of 64 units?

Ans:5
Side of 1st cube = (729)1/3 = 9 unitsRadius of the cone = 2 X 9 = 18 units

 

Side of 2nd cube = (64)1/3 = 4 units

Height of the cone = 2 * 4 = 8 units

Volume of the cone = ⅓ πr2h

= ⅓ π x 18 x 18 x 8

= 864π units

8. When 4 dice are thrown then what is the probability the same number appears on each of them?

Ans:2
Total number of outcomes when 4 dice are thrown = 64There are 6 cases namely; (1, 1, 1, 1) , (2, 2, 2, 2), (3, 3, 3, 3), (4, 4, 4, 4), (5, 5, 5, 5) and (6, 6, 6, 6).

 

Hence required probability = 6/64 = 1/216

9. An increment of 2.4 percentage points in the rate of simple interest causes an additional income of Rs 7500 for 5 years. What is the principal amount?

Ans:2
Let the principal amount be Rs P.
Additional interest obtained due to 2.4 percentage point increase in rate of interest and time is 5 years = (2.4 X 5 X P)/100 = Rs 12P/100
According to the question, 12P/100=7500

10. In a Company, the average salary of the managers is 65000 and the average salary of the engineers is 30000. If the ratio of the number of managers and engineers is 4 : 3, then what is the average salary of the employees of the company? (Assume the company has only managers and engineers)

Ans:4
Let the number of Managers be 4n and the number of engineers be 3n.
So, the total salary of managers = 65000 x 4n = 260000n
And the total salary of engineers = 30000 x 3n = 90000n
So the total salary of Engineers + managers = 350000n
And total number of employees = 4n + 3n = 7n
So the average salary of the company = 350000n/7n = Rs 50000

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