**1. The HCF and LCM of two numbers are 21 and 4641 respectively. If one of the number lies between 200 and 300, then the two number are –**

(a) 273, 357

(b) 273, 361

(c) 273, 359

(d) 273, 363

**Sol:**

**Product of the numbers**

**= HCF×LCM**

**= 21×4641**

**=21×3×7×13×17**

**=3×7×3×7×13×17**

**i.e. 273 and 357.**

**2. A number when divided by 765 leaves a remainder 42. What will be the remainder if the number is divided by 17?**

(a) 8

(b) 5

(c) 7

(d) 6

**Sol:**

**Let the number be x**

**∴ x=765k+42**

**=> 17×45K+17×2+8**

**=>17(45K+2)+8**

**17(45K+2)+8**

**Remainder=8**

**3. The hands of a clock are 10 cm and 7 cm respectively. The difference between the distance traversed by their extremities in 3 days 5 hours is –**

(a) 4552.67 cm

(b) 4557.67 cm

(c) 4555.67 cm

(d) 4559.67 cm

**Sol:**

**Distance traversed by the extremity of the minute-hand in one hour=2×22/7×10**

**Distance traversed by the extremity of the minute-hand in 3 days and 5 hour, i.e. in 77 hours**

**=2×22/7×10×77**

**=> 22×220 = 4840 cm**

**Distance traversed by the hour-hand in 12 hour=2×22/7×7=44 cm**

**Distance traversed by the hour-hand in 77 hour=44/12×7=(11×77)/3=847/3=282.33 cm**

**Reqd. difference =4840-282.33=4557.67 cm**

**4. If the ratio between the sum of a n terms of two arithmetic progressions is (7n + 1): (7n + 27), find the ratio of their 11th terms –**

(a) 148 : 113

(b) 147 : 118

(c) 148 : 111

(d) 147 : 111

**Sol:**

**(c)**

**5. In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?**

(a) 0

(b) 2

(c) 3

(d) 7

**Sol:**

**(c)**

**6. Ratio of Ashok’s age to Pradeep’s age is 4:3. Ashok will be 26 yr old after 6 yr. How old is Pradeep now?**

(a) 18 yr

(b) 21 yr

(c) 15 yr

(d) 24 yr

**Sol:**

**Ashok’s present age = 26-6=20 yrs**

**∴ Pradeep’s present age = 20×3/4=15 yrs**

**7. In the clas of 52 students, the number of boys is 2 less than number of girls. The average weight of the boys in 42 kg. while the average weight of all the student is 52 kg. What is the average weight (in kg) of the girls?**

(a) 61

(b) 39

(c) 80

(d) 68

**Sol:**

**Let the number of girls=x**

**boys=x-2**

**According to question:-**

**x+x-2=52**

**∴x=27**

**∴ NO. of bags=25**

**Again:-**

**Let average no. of girls=y kg**

**42×25+27xy=52×52**

**∴y=(52×52-42×25)/27**

**=61.25~61 Kg (Approx.)**

**8. A mathematics teacher calculated the total marks obtained by 35 students of 8th class. The average marks of the students was 72. But 36 marks of Reena was calculated in palce of 86 obtained by her. What was the correct average of all the students?**

(a) 73.14

(b) 74.31

(c) 72.43

(d) 73.42

**Sol:**

**Wrong calculated marks**

**=35×75=(2520-36+86)/35=2570/35=73.42**

**9. Several litres of acid were drawn off a 54 l vessel full of acid and an equal amount of water added. Again, the same volume of mixture was drawn off and replaced by water. As a result the vessel contained 24 l of pure acid. How much of the acid was drawn off initially?**

(a) 12 l

(b) 16 l

(c) 18 l

(d) 24 l

**Sol:**

**If a container contains y units of liquid and x units of liquids is taken out. If this operation is repeated n times. The final quantity of the liquid in the container is**

**y(1-x/y)^n**

**∴24=54(1-x/54)^2**

**=> (1-x/54)^2=24/54=4/9**

**=> (1-x/54)=2/3**

**=> x/54=2/3**

**x=18 l**

**10. 5 l water is added to certain quantity of pure milk costing Rs 3/l. If by selling the mixture at the same price as before, a profit of 20% is made, then what is at the amount of pure milk in the mixture?**

(a) 20 l

(b) 30 l

(c) 25 l

(d) 35 l

**Sol:**

**Let the quantity of pure milk be x l.**

**If 5 l of water is added to it.**

**Then,**

**Cost of (5+x)l**

**=Rs.(3x+5)**

**∴ Profit =Rs.15**

**Given, 20% of 3x=15**

**=> 3x/5=15**

**x=25 l**

**Answers will be updated soon….**