**Q.1.**A vessel is filled with liquid, 4 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

(1) 1/9

(2) 1/11

(3) 1/10

(4) 3/10

(5) None of these

**Answer: 3**

**Solution:**

Suppose the vessel initially contains 9litres of liquid.

Let x litres of this liquid be replaced with water.

(4-(4x/9) +x) = (5-(5x/9))

X = 9/10

So, part of the mixture replaced = 9/10 × 1/9 = 1/10

**Q.2.**If 4 men working 4 hours per day for 4 days complete 4 units of work, then how many units of work will be completed by 2 men working for 2 hours per day in 2 days?

(1) 1

(2) 2

(3) 0.5

(4) 3

(5) None of these

**Answer: 3**

**Solution:**

Formula used M1D1H1/W1 = M2D2H2/W2

(4×4×4)/4 = (2×2×2)/W

W = 0.5units

**Q.3.**Shantanu borrowed Rs. 2.5 lakh from a bank to purchase one car. If the rate of interest be 6% per annum compounded annually, what payment he will have to make after 2 years 6 months?

(1) Rs. 189315

(2) Rs.

Source: safalta.com

389335(3) Rs. 489425

(4) Rs. 289325

(5) None of these

**Answer: 4**

**Solution:**

CI for 2 years 6 months at the rate of 6,

Applying the net% effect for first 2 years = 6 + 6 + (6 × 6)/100 = 12.36%

Rate of interest for 6 months = (6/12) ×6 = 3%

For next 6 months = 12.36 + 3 + (12.36×3) /100 = 15.36 + 0.37% = 15.73%

Here, we can see that in 2 years 6 months the given compound rate of interest is approximate 15.73%.

Now, 115.73% of 250000 = (115.73×250000)/100 = 289325

**Q.4.**The average of eight numbers is 25, out of which average of first two numbers is (39/2) and the average of the next three numbers is (70/3) . The sixth number is less than the seventh and the eighth by 5 and 8 respectively. Find the seventh number.

(1) 31

(2) 33

(3) 35

(4) 37

(5) None of these

**Answer: 1**

**Solution:**

Sum of eight numbers = 25×8 = 200

Sum of first two numbers = (39/2) ×2 = 39

Sum of first three numbers = (70/3) × 3 = 70

Let, the sixth number be x

So, sum of sixth, seventh and eighth number = 200 – (39+70) = 200 – 109 = 91

= x+x+5+x+8 = 91

= x = 26

Therefore, seventh number = 26 + 5 = 31

**Q.5.**Two places are 60 km apart. A and B start walking towards each other at the same time and meet each other after 6 hours. Had A travelled with 2/3rd of his speed and B travelled with double of his speed, they would have met after 5 hours. Find the speed of A?

(1) 6 km/h

(2) 4 km/h

(3) 5 km/h

(4) 8 km/h

(5) None of these

**Answer: 1**

**Solution:**

Let speed of A = x km/h and speed of B = y km/h

x + y = 60/6 = 10km/h …….(1)

2/3 x + 2y = 60/5 = 12 km/h …….(2)

From 1 and 2 we get

x = 6 km/h and y = 4 km/h

**Q.6.**A man would gain 25% by selling a chair for Rs. 47.5 and would gain 15% by selling a table for Rs. 57.5. He sells the chair for Rs. 45; what is the least price for which he must sell the table to avoid any loss on the two together?

(1) Rs. 41.2

(2) Rs. 42.2

(3) Rs. 43

(4) Rs. 45.2

(5) None of these

**Answer: 3**

**Solution:**

Cost Price of chair = 100/125 × 47.5 = 38 Rs.

Cost Price of table = 100/115 × 57.5 = 50 Rs.

Required SP of table = (50 + 38) - 45 = 43 Rs

**Q.7.**The cost of Type 1 rice is Rs. 30 per kg and Type 2 rice is Rs. 40 per kg. if both Type 1 and Type 2 are mixed in the ratio of 1 : 4, then what will be the price per kg of the mixed variety of rice?

(1) 38 Rs/kg

(2) 34 Rs/kg

(3) 48 Rs/kg

(4) 58 Rs/kg

(5) None of these

**Answer: 1**

**Solution:**

Mean price = (30×1+40×4)/5 = 38 Rs/kg

**Q.8.**In a plane there are totally 8 points (no three points are collinear), how many lines can be drawn?

(1) 28

(2) 24

(3) 64

(4) 56

(5) None of these

**Answer: 2**

**Solution:**

To draw a line we need 2 points. From the given 8 points , we need to choose 2 points Number of ways in which this can be done is 8C2= 28

**Q.9.**A circular wire of radius 49 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 4:7. Find the smaller side of the rectangle?

(1) 56 cm

(2) 48 cm

(3) 35 cm

(4) 42 cm

(5) None of these

**Answer: 1**

**Solution:**

Circumference = 2×(22/7)×49 = 308 cm

Lengths of rectangle sides are 4x, 7x.

Circumference = 2× (4x+7x)

308 = 22x

x = (308/22) = 14

Smaller side of rectangle = 4x = 4×4 = 56 cm

**Q10.**A bag contains 7 red, 5 green and 6 blue balls. Three balls are drawn one by one at random without replacement. Find the number of ways that the first ball is red, second ball is green and third ball is blue?

1) 31/512

2) 35/816

3) 33/713

4) 34/812

5) None of these

**Answer: 2**

**Solution:**

Reqd. probability = | 7 | × | 5 | × | 6 | = | 35 |

18 | 17 | 16 | 816 |

Reqd. probability = | 7 | × | 5 | × | 6 | = | 35 |

18 | 17 | 16 | 816 |