**Find solutions for all the questions at the end of each set:**

### Set A

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

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

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

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

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

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

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

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

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

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

Answers and solution:

1. (a); 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); Let the number be x

∴ x=765k+42

=> 17×45K+17×2+8

=>17(45K+2)+8

17(45K+2)+8

Remainder=8

3. (B)

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. (c)

5. (c)

6. (c); Ashok’s present age = 26-6=20 yrs

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

7. (a); 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. (d) Wrong calculated marks

=35×75=(2520-36+86)/35=2570/35=73.42

9. (c); 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. (c) 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

**Find solutions for all the questions at the end of each set:**

### Set B

1. An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from the usual speed. Find its usual speed.

(a) 300 km/hr

(b) 500 km/hr

(c) 400 km/hr

(d) 200 km/hr

2. Three girls Sangeeta, Namrata and Mandip are playing a game by standing on circle of radius 5 m drawn in a park. Sangeeta throws a ball to Namrata, Namrata to Mandip, Mandeep to Sangeeta. If the distance between Sangeeta and Namrata and between Namrata and Mandip is 6 m each, what is the distance between Sangita and Madip?

(a) 7.6 m

(b) 8.6 m

(c) 9.6 m

(d) 4.6 m

3. How many of the following numbers are divisible by 132?

264,396,4,762,792,968,2178,5184,6336

(a) 4

(b) 5

(c) 6

(d) 7

4. If the numerator and the denominator of a proper faction are increased by the same quantity, then the resulting fraction is

(a) always greater than the original fraction

(b) always less than the original fraction

(c) always equal to the original fraction

(d) None of the above

5. There are five numbers. HCF of each possible pair is 4 and LCM of all the five numbers is 27720. What will be the product of all the five numbers?

(a) 7096320

(b) 7906320

(c) 7096230

(d) 7903620

6. In the class of 100 students, the number of students passed in English is 46, in Maths is 46 and in Commerce is 58. The number who passed in English and Maths is 16, Math s and commerce is 24 and English and commerce is 26, and the number who passed in all subjects is 7. Find the number of the students who failed in all the subjects.

(a) 13

(b) 8

(c) 9

(d) 7

7. On reducing the entry fee by 25% in a circus show, the number of viewers increased by 30%. The percent increase or decrease in the income from the entry fee is

(a) 2.5 % increase

(b) 0.5% decline

(c) 2.5% decline

(d) 3% increase

8. If 60 is subtracted from a number it is reduced by 80%. The 2/3 rd of the number is

(a) 75

(b) 50

(c) 100

(d) 60

9. A person bought certain quantity of rice at the rate of Rs. 150 per quintal. 10% of the rice was spoiled. At what price (per quantal) should he sell the remaining rice to earn 20% profit?

(a) Rs.200

(b) Rs. 180

(c) Rs. 225

(d) Rs.175

10. A sells a good to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays Rs. 225 for it, what is the cost price of A?

(a) Rs. 200

(b) Rs. 150

(c) Rs. 175

(d) Rs. 175

Answers Key:-

1.(b)

2.(c)

3.(a)

4.(a)

5.(a)

6.(c)

7.(c)

8.(b)

9.(a)

10.(b)

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