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) = **

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