**CMAT Quantitative Aptitude Practice questions Set-2:** This practice set has 10 questions with their answers covering topics from the areas of Quantitative Aptitude. This Practice set includes the Questions as per the CMAT Exam pattern and syllabus.

**1.** The ratio between Rohit’s and Vivek's age at present is 5:3. Vivek is 8 years younger than Rohit. The ratio of Rohit’s age to Vivek's age after 5 years will be :

a) 21 : 17

b) 19 : 12

c) 25 : 17

d) None of these

**2.** A circular cake of radius 15 cm is to be shared by 6 people consisting of 4 children and 2 adults. Cake is divided equally for individual child and similarly for adults The area of the piece given to adults is 82.5 cm^{2}. Find the angle contained by cake slice of child.

a) 69°

b) 46°

c) 83°

d) 38°

**3.** There are some coins and plates of either silver or gold in a box. 40% of the objects are coins, 60% of the plates are of silver and 30% of the coins are of gold. What is the percentage of silver articles?

a) 64

b) 68

c) 52

d) 48

**4.** A person bought 76 articles and sold 20 articles at 15% profit, 40 articles at 19% profit and remaining 16 articles at 25% profit and got a profit of Rs 6570 as a whole. The cost price of each article is:

a) Rs 450

b) Rs 425

c) Rs 420

d) Rs 400

**5.** If m = 12 and n = -3, then 16m^{2} - 24mn + 9n^{2} =

a) 3249

b) 2047

c) 3468

d) 4142

**6.** A basket has 6 apples, 4 oranges, 2 bananas and 3 mango, if two fruits are picked randomly, what is the probability that both are apples?

a) 1/6

b) 1/3

c) 2/15

d) 1/7

**7.** A hollow iron pipe is 28 cm long and its external diameter is 14 cm. If the thickness of the pipe is 2 cm and iron weighs 9 gms/cm^{3} , then the weight of the pipe is:

a) 26.56 kg

b) 21.65 kg

c) 28.11 kg

d) 23.76 kg

**8.** Without stoppage, a train travels a distance of 120 km in 2 hours. and with stoppage it covers the same distance with an average speed of 40Km/hr. On an average, how many minutes per hour does the train stop during the journey?

a) 12 minutes

b) 15 minutes

c) 18 minutes

d) 20 minutes

**Directions (9 -10)** Two different banks declare fixed annual rate of interest on the amounts invested by the people under a special scheme launched by the government to encourage savings. The rate of interest offered by these banks may differ from year to year depending on the market forces of the economy. The annual rate of interest offered by the two banks State bank of India (SBI) and Bank of Baroda over the years is shown by the line graph provided below.

**9.** A household invested a sum of Rs 23 lakhs in Bank of Baroda 2008. The total amount received after one year was re-invested in the other bank for one more year. The total interest received by the household on his investment was?

a) 4,89,000

b) 4,70,350

c) 5,01,500

d) 5,10,500

**10.** An investor invested Rs. 5 lakhs in SBI in 2008 as fixed deposit at the existing interest rate on simple interest for three years, calculate the difference in his earnings if he does not make the fixed deposit and the received the varying interest for the next three years.

a) 7500

b) 6800

c) 8500

d) None of these

**Answer Key:**

**1.** (c) **2.** (a) **3.** (a) **4.** (a) **5.** (a) **6.** (d) **7.** (d) **8.** (d) **9.** (b) **10.** (a)

**Explanations:**

**Explanation 1:**

Let their ages be 5x and 3x years.

5x - 3x = 8 or x = 4

Rohit's age = 20 years, Vivek's age = 12 years

Ratio of their ages after 5 years = 25 : 17

**Explanation 2: **

The pieces of cake will be in form of sectors of circle.

Let R be the radius of cake and θ_{a}, θ_{c} be the angle of sectors of adults and children respectively.

The area of the piece given to adults = 82.5 cm^{2}

θ_{a}/360 πR^{2} = 82.5

θ_{a}/360 π15^{2} = 82.5

θ_{a} = 42

Also,

2θ_{a} + 4θ_{c} = 360

θ_{a} + 2θ_{c} = 180

42 + 2θ_{c} = 180

θ_{c} = 69°

**Explanation 3:**

**Explanation 4:**

Let the cost price of each article be Rs x each.

20 × 15x/100 + 40 × 19x/100 + 16 × 25x/100 = 6570

300x + 760x + 400x = 6570 × 100

x = 6570 × 100/1400 = Rs 450

**Explanation 5:**

16m^{2} - 12mn + 9n^{2}

= 16 × 12^{2} - 24 × 12 × - 3 + 9(-3)^{2}

= 16 × 144 + 24 × 36 + 9 × 9

= 2304 + 864 + 81

= 3249

**Explanation 6:**

Total number of fruits = 15

Way of selection of two apples = ^{6}C_{2}

Way of selection of two apples = ^{6}C_{2}

So, required probability = 6 × 5/15 × 14 = 1/7

**Explanation 7:**

External radius = 7cm,

Internal radius = 5 cm.

Volume of iron = 22/7 × (7^{2} - 5^{2})× 35 = 2640 cm^{3}

Weight of iron = (2640 × 9)gm = 23760 gm = 23.760 kg

**Explanation 8:**

Without stoppage, average speed of the train = 60 km/hr means it speed per minute = 1 km.

With stoppage it covers the same distance with an average speed of 40Km/hr means it travel only for 40 minutes.

**Explanation 9:**

23 lakhs × 9.5/100 + 25.185 × 10/100

2, 18,500 + 2, 51,850

4, 70,350.

**Explanation 10:**

Interest received from Fixed deposit = 5 lakhs × 8 ×3/100 = 1.2 lakhs

Interest received on yearly basis = 5 lakhs × 8/100 + 5 lakhs ×10/100 + 5 lakhs × 7.5/100 = 1.275 lakhs

Difference = 7500

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