- 1. Five years ago, the sum of my age and my mother's age was equal to my father's age. If my father is 6 years elder than my mother, find my present age

**Answer: Option 'B'**

**Let my present age be X
Let the age of my mom as M
Let the age of my father as F
So, According to question
(X - 5) + (M - 5) = (F - 5),
X + M = F + 5
X = F - M + 5
F - M = 6
X = 6 + 5 = 11**

- 2. The sum of the ages of Sandya and Avanthi is twice the difference of their ages. Find the ratio of Avanthi's age to Sandya's age.

**Answer: Option 'C'**

**Lets the age of Sandya as S
Lets the age of Avanthi as A
S + A = 2(S - A)
S + A = 2S - 2A
3A = S
A/S = 1/3
A : S = 1 : 3
**

- 3. The area of the largest square that can be inscribed in a circle of radius 5 cm is

**Answer: Option 'C'**

**Radius = 5cm
so side of the square is 5cm,
therefore => Diagonal of the square = Diameter of the circle ?2 a = 2r = 10cm a**

- 4. In a rectangular hall of length 12m and breadth 8m, the sum of the areas of the floor and the ceiling is equal to the sum of the area of the four walls. Find the height of the hall.

**Answer: Option 'D'**

**Length = 12m
breadth = 8m, according to the question
sum of the area of floor and celling = sum of area of four wall(let h is the height of the wall)
=>2 × 12 × 8 = (2 × 12h) + (2 × 8h) h = 4.8m**

- 5. In a to and fro journey between two places, the average speed of a boat was 9.1 kmph. If the upstream speed of the boat is 7 kmph, find the speed of the stream.

**Answer: Option 'C'**

**Let, upstream speed as u
Downstream speed as d
Speed of the stream as s,
So
u = b - s
=> d = b + s
Average speed = 2ud/(u + d)
=> (2 × 7 × d)/(7 + d) = 9.1
= 14d = 9.1(7 + d)
On solving we get,
=> d = 13 kmph
=> s = (d-u)/2 = 3 kmph**

- 6. Which of the following fractions is greater than 3/5 and less than 6/7?

**Answer: Option 'C'**

**3/5 = 0.667 = 0.85 (Taken only the first two digits after the decimal point)
Hence, the question is to find out a number which is greater than 0.6 and less than 0.85
The given choices are
1/2 = 0.523 = 0.66 (Taken only the first two digits after the decimal point)
1/3 = 0.33 (Taken only the first two digits after the decimal point)
7/8 = 0.87 (Taken only the first two digits after the decimal point)
Clearly, 0.66 = 2/3 is the answer**

- 7. Mohinder and Surinder entered into a partnership investing Rs.12000 and Rs. 9000 rep. After 3 months Sudhir joined them with an investment of Rs. 15000. What is the share of Sudhir in a half-yearly profit of Rs. 9500?

**Answer: Option 'C'**

**1. Total length of the period = 6 month
2. After 3 months Sudhir joined, therefore his length of period is 3 months
3. Find the profit ratio
12000 × 6 : 9000 × 6 : 15000 × 3
72000 : 54000 : 45000
(divide by 1000 and then divide by 9)
8 : 6 : 5
4. Sudhir's share = 5/19 × Rs. 9500 = Rs. 2500/-
**

- 8. An inlet pips fills a tank at the rate of 5 litres of water a minute. An outlet connected to the tank can empty a fulltank in 5 hours. Both the pipes are opened together for 30 minutes and then, the outlet is closed. It took another 36 minutes to fill the tank. Find the capacity of the tank.

**Answer: Option 'B'**

**Let the inlet pips take X minutes to fill the tank.
Part of the tank filled by the inlet in a minute = (1/x)
Part of the tank emptied by the outlet in a minute = 1/(5*60) = 1/300
Part of the tank filled in the first 30 minutes = 30×[(1/x)-(1/300)] = (300 - X)/10x
Part of the tank filled in the next 36 minutes = 36*(1/x) 1 - [(300 - x)/10x] 36/x Solving,
x = 60 Capacity of the tank = 60 × 5 = 300 liters
**

- 9. An empty drum can be filled with 18 buckets of water, if the capacity of each bucket is 16 liters. How many buckets will be need to fill the drum if the capacity of each bucket is 12 litres?

**Answer: Option 'C'**

**Capacity of the drum = 18 × 16 = 288 liters
No. of buckets needed = 288/12 = 24 liters**

- 10. The proportion of milk and water in 3 samples is 2 : 1, 3 : 2 and 5 : 3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is

**Answer: Option ''**

**Proportion of milk in the 3 samples is (2/3), (3/5), (5/8)
Proportion of water in the 3 samples is (1/3), (3/5), (3/8) Equal quantities of the three samples are taken.
Proportion of milk in the mixture = (2/3) + (3/5) + (5/8) = 227/120
Proportion of water in the mixture = (1/3) + (2/5) + (3/8) = 133/120
Proportion of milk and water = (277/120)/(133/120) = **

- 11. The greatest 4-digit number which is divisible by 6, 8 and 10 is

**Answer: Option 'B'**

**For a number to be divisible by 6, 8 and 10, It should be divisible by theiir LCM.
LCM(6, 8, 10) = 120
To find the greatest 4 - digit number divisible by 120,
divide 9999 by 120 and find the remainder
Remainder = 39
â€‹9999 - 39 = 9960**

- 12. A jar contains 10 liters of milk. After selling 1 liter of milk, the milkman adds 1 liter of water to the jar. He repeats the process again. What is the percentage of milk contained in the jar now?

**Answer: Option 'B'**

**Amount of milk after 2 operations = 10[1 - (1/10)] ^{2} = 10 × (9/10) × (9/10) = 8.1 litres
% of milk = (8.1/10) × 100 = 81%**

- 13. A student finds the average of 10 positive integers. Each integer contains two digits two digits. By mistake, the boy interchanges the digits of the one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?

**Answer: Option 'D'**

**Let the original number be ab (10a + b)
After Interchanging the digits,
it becomes ba (10b + a)
Average = Sum/n
n = 10 Sum = 10*Average Since the average decreases by 1.8,
the sum of the numbers will decrease by 18.
(10b + a) = (10a + b) - 18
9b = 9a - 18
a - b = 2**

- 14. A shepherd has 1 milion sheeps at the beginning of the year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheeps die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheeps. Which of the following is correct?

**Answer: Option 'A'**

**Let x = 10.
The sheep population increases by 10% during the year 2000.
Sheep population at the beginning of 2001 = 1.1million
Sheep population decreases in 2001 and reaches 1 million.
% decrease = [(1.1 million - 1 millon)/1.1 million] × 100 = (0.1/1.1) × 100 = 9.09%
y = 9.09%
x>y**

- 15. A and B entered into a partnership investing Rs. 16000 and Rs. 12000 resp. After 3 months A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs.26,400 after one year by

**Answer: Option 'C'**

**1. Investment of A = Rs. 16000 × 3 + Rs. 11000 × 9
= Rs. 147000 (Since he withdrew Rs. 5000 after 3 months)
2. Investment of B = Rs. 12000 × 3 + Rs. 17000 × 9
= Rs. 189000 (he invested Rs. 5000 more after 3 months)
3. Investment of C = Rs. 21000 × 6 = Rs. 126000 (He joined after 3 more months)
4. Profits ratio = 147 : 189 : 126 ; 7 : 9 : 6
5. Share of B = 9/22 × 26400 = Rs. 10800/6.
Share of C = 6/22 × 26400 = Rs. 7200.
Share of B exceeds that of C
= Rs. 10800 - Rs. 7200
= Rs. 3600/-**

- 16. X and Y invested in a business. They earned some profit which divided in the ratio of 2 : 3. If X invested Rs. 40000, the amount invested by Y is

**Answer: Option 'C'**

**1. Rs. 40000 : investment of Y = 2 : 3
2. 40000/- investment of Y = 2/3
3. 120000 = 2 x investment of Y
4. Investment of Y = 120000/2
= Rs. 60000/-**

- 17. The speed of a boat in still water is 8 kmph and the speed of the stream is 2 kmph. The boat travels to an island at a distance of 30 km, stays there for 2 hours and returns to the starting point at 5:00 pm. At what time did the boat start to the island?

**Answer: Option 'A'**

**Upstream speed (u) = b - s = 6 kmph,
Downstream speed (d) = b + s = 10 kmph,
Time taken to travel upsteam = 30/6 = 5 hours.
Time taken to travel downstream = 30/10 = 3 hours
Time in island = 2 hours
Total time = 10 hours,
Therefore, the boat should have started at 7 in the morning.**

- 18. The effective speed of a boat is 10.5 kmph against the stream and 16.5 kmph along the stream. Find the speed of the stream.

**Answer: Option 'B'**

**upstream speed (u) = 10.5 kmph,
Downstream speed (d) = 16.5 kmph,
Speed of the stream(s) = (d-u)/2 = 3 kmph**

- 19. John can row at a speed of 6.8 kmph in still water. If the speed of the stream is 3.2 kmph, find the time taken by him to row 15 km downstream.

**Answer: Option 'B'**

**Speed of the john in still water = 6.8 kmph
Speed of the stream = 3.2 kmph
Downstream speed = 6.8 + 3.2 = 10 kmph
Time taken => distance/speed 15/10 = 1.5 hours**

- 20. A boat moves at 8 kmph in still water. If the speed of a stream is 2.1 kmph, find the effective speed with which the boat travels upstream.

**Answer: Option 'B'**

**Upstream speed = 8 - 2.1 = 5.9 kmph**

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