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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?

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?

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.

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

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?

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?

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?

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

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?

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)

**Check your Answers below:**

##### 1. Question

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. Question

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. Question

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. Question

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. Question

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. Question

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. Question

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 1^{st}cube = (729)^{1/3}= 9 unitsRadius of the cone = 2 X 9 = 18 unitsSide of 2

^{nd}cube = (64)^{1/3}= 4 unitsHeight of the cone = 2 * 4 = 8 units

Volume of the cone = ⅓ πr

^{2}h= ⅓ π x 18 x 18 x 8

= 864π units

##### 8. Question

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 = 6^{4}There 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 = 6/6

^{4}= 1/216##### 9. Question

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. Question

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