10 June Maths Ii

Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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A ladder leaning against a vertical wall makes an angle of 45 degree with the ground. The foot of the ladder is 3 meters from the wall. What is the length of ladder? A

• Let us assume that Ladder is AB • There is an angle of 45 Degree at the angle A. Now here we have Hypoteneusse divided by base should be 2^1/2 because Sec 45 degree is equal to 2^1/2. H/B=2^1/2; H / 3 = 2^1/2 • H=3*2^1/2 • Hypoteneuse (length of ladder) = 4.2 m. approx.

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Answer continued:… standard values Angle 0

Sin 0

Cos 1

Tan 0

30

1/2

3^1/2/2

1/3^1/2

45

½^1/2

½^1/2

1

60

3^1/2/2

1/2

3^1/2

90

1

0

Infinite

180

0

-1

0

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Answer continued.. • • • • • •

Sin = Perpenditular / Hyp. Cos = Base / Hypoteneuse Tan = Perp. / Base Opposite of Sin is cosec Opposite of Cos is Sec. Opposite of Tan is cot. www.afterschoool.tk

The pilot of a helicopter at an altitude of 1200 m. finds that 2 ships are sailing towards it in the same direction. Angles of dipression of ships are 60 and 45 degrees. What is the distance between ships?

• Perpendicular = 1200 • We have to find base. We will use Cot 45 & cot 60. Cot 45 = Base / Per =1, Base = 1200 Cot 60 = Base / per = 1/3^1/2; Base = 1200/3^1/2 = 692. Distance between ships = 1200-692 = 508 meters ans. www.afterschoool.tk

Hel

A baloon is connected through a cable. The length of cable is 200 m. the baloon is inclined at 60 degrees to the horizontal. What is the height of baloon?

• • • • • • •

B

200 m

Hypoteneuse is 200 m. We have to find perpendicular We will use Sin 60 = 3^1/2 / 2 P/ 200 =3^1/2 / 2 P =3^1/2 *100 P = 173.2 Height of baloon is 173 meters approx. www.afterschoool.tk

A,B,C,D, are 4 consecutive odd numbers. What must be added to the product ABCD to make it a perfect square: Options are: 1,4,8,16

• 16 (solve by hit and trials).

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Find the chance of throwing less than 16 in a throw of 3 dice? • Total number of possibilities in three throws: 6*6*6 = 216 • It is better to find chances of having 16 or more than 16. the possibilities are limited : 664,646,466,655, 565,556,665, 656,566,666, • Other possibilities are 216-10= 206 • Thus probability is 206 / 216 = 103/108 ans.

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The mean proportional between 8 & 72? • • • • •

For proportional questions, find GM. GM of 8 & 72 8*72 = 576 Squre root of 576 = 24 Mean proportional is 24

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2 trains are moving towards each other @ 60 km p.h. each. They are 400 km apart. A bird is moving from one train towards other @ 100 km p.h. How long will the bird take to reach the 2nd train?

• The combined speed of 2 trains is 120 km p.h. • For bird, we will combine speed of bird and 2nd train = 160. • 400/160 = 2.5 hours. Ans.

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In the previous question, the bird returns back to the first train after reaching 2nd train. What is the total time of the bird from 1st to 2nd and back to 1st?

• The bird has already travelled for 2.5 hours (250 km.). The 1st train has also travelled for 60*2.5 = 150 km. • Now the bird will have to travel 250-150 = 100 km. only to reach back the first train. The combined speed is 160. 100/160*60 = 37.5 minutes thus the bird will take 3 hours, and 7.5 minutes to return back to the first train. www.afterschoool.tk

If the bird keep shunting between the two train like this till the two trains meet, how much does bird travel? • • • • • • •

The bird has already travelled: 2.5*100 = 250 Km 37.5/60 *100 =62.5 Km. Now the bird will again travel towards 2nd train: the distance to be covered is 62.5 – 37.5= 25 km. 25/160*60 =9.375 minutes The bird will travel 15.62 km. He will have to travel again back 15.62- 9.375 = 6.245 Km. He will will again travel back to 1st train by 160 speed.

We can observe that these values are in GP. Therefore there is no need of this much of calculation. We can solve it as infinite series. The answer is : 250 / (1-.25) = 250/.75 = 333.33 Km ans.

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The diagonals of a rhombus are 24 & 10. What is the length of its side? • Apply pythogorus rule, take any quadrant. One quadrant has one side as 12 and other as 5. applying pythogorus rules, we get 13 as answer. • (12^2 +5^2) = 169 • Square root of 169 is 13.

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Speed of a train is 63 km per hour. It takes 8 seconds to cross a tree and 20 seconds to cross a platform. What is the length of platform?

1. Convert speed into m/sec. Multiply speed by 5/18 = 63*5/18 =17.5 m/s 2. Distance covered in 8 sec = 17.5*8 = 140 meters. (length of the train) 3. Distance covered in 20 sec. = 17.5*20 = 350 Platform = 350-140= 210 m. www.afterschoool.tk

A person covers a distance @75 km / hour and returns (same distance) @ 50 km/ hour. What is his average speed?

• We have to calculate harmonic mean of 50 & 75. • Add 1/50 +1/75 = 125/3750 • Multiply these by ½ = 125/7500 • =1/60 • Reverse it , answer is 60 km / hour. Ans. www.afterschoool.tk

An aeroplane travels distances of 2500 km 1200km, 500 km 400km at speeds of 500, 400 , 250 km per hours. What is its average speed?

• Average speed = Total distance / total time • 4200 is total distance • Total time: 2500/ 500, + 1200/400 +500/250 = 10 hours • 4200 / 10 = 420 km p/h

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A person can row upstream @8 km / hour and downstream 10.6 km / hour what is the speed of person and water?

• Speed of water: 10.6-8 =2.6 divided by 2 = 1.3 km /h • 8+1.3 = 9.3 speed of person.

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A can do a piece of work in 20 days. He worked for 2 days. Then B complted remaining work in 9 days. How much time will be taken by B in completing the entire work alone?

• • • • •

A’s one day’s work = 1/20 2 days’ work = 2/20 =1/10 Remaining work = 9/10 B’s one day’s work = 9/10 *1/9 =1/10 Thus B will be able to complete the work in 10 days.

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Put these in ascending order? 3/8, 7/16, 5/12 1/6 • 3/8 is equal to 6/16 therefore it is smaller to 7/16. • 1/6 is equal to 2/12, therefore it is saller to 5/12. • LCM of 16 & 12 is 48, multiply it to all the numbers, • We get 18, 21, 20, 8, • The ascending order: 1/6, 3/8, 5/12, 7/16 ans.

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A:B 2:3, B:C = 5:9 A:B:C? 2:3, • A:B B:C = 5:9 • • the ratio (using multiplyin approach). • 10:15:27. ans.

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Price of Petrol 30%, how much should consumtpion be reduced to keep the budget the same? • • • •

Increase in consumption 100 to 130 Reduce it from 130 to 100 Means 30 on 130 30/130 *100 = 23.1% approx. ans.

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2/5th of a property is worth 10000. what is the worth of 7/10th of that property? 2/5 is eqaul to 4/10 We have to get 7 against 4. 7/4*10000 = 17500 ans. Total value of property = 5/2*10000 = 25000 • 7/10th is 1/10 *25000 = 17500 • • • •

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A business person has 20% margin, he gives 10% discount. What is his net profit in %?

• • • •

100 + 20 = 120 Discounting 10% 120 – 12 = 108 Gain is 8 %ans

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65% students pass in English, 56% pass in Maths. 25% failed in both the papers. What % passed in both?

• • • • •

100-25 = 75 65+56 – X = 75 -X=75-121 X= 46% 46 % passed in both the papers.

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In how many ways can 36 be written as a product of two natural numbers? • • • •

Factors: 1,2,3,4,6,9,12,18,36 1*36; 2*18, 3*12, 4*9,6&6 Thus there are 5 ways.

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In how many ways can 36 be written as a product of two integers? • 10 possibilities • (5 + 5) (negative numbers are also included).

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The value of a number is 5 times the sum of its digits. Which is the number: 36,27,45,18

• 45 ans.

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Afterschooolian Raju spends ¼ of working time in reading, 2/3rd of remainign time on TV. Suppose he spends 4 hours on TV. What is his working time?

• • • •

Remaining time ¾ 2/3 of ¾ = 6/12 Thus he spends ½ time on TV, Total working time with him = 8 hours. www.afterschoool.tk

How many numbers are there between 200 &300which have only one 5? • There are 9 as 205, 215, 225 and so on (don’t take 255). • 250,251,252,253,254,256,257,258,2 59 • Total = 18 ans.

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Divide 417 among ABCD,, A gets 13>B, B gets 9 >C, and c should get 6> D. What the shares of A,B,C,D? • • • • • • • •

Let us assume that D get X. C gets X +6 B gets X+ 15 A Gets X + 28 X+X+6+X+15+X+28 = 417 4X=417-49 X = 368/4 = 92 A = 120, B =107, C = 98, D = 92 Ans.

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Afterschooolian Rajesh takes a loan of Rs. 2 Crore and gave them as micro credit (micro finance) @5% and gives loan to poor people at 4% for 6 years. He pays at simple interest and charges compound interest. What is his loss in %?

Let us do calculation on 100 Rs. Simple interest for 3 years = 30. Compound interest for 3 years is : 1.04*1.04*1.04*1.04*1.04*1.04 – 1 = .265319 • The % loss is .035% in six years or approximately .006% per annum. • • • •

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A train @ 72 km p/h. it takes 7 seconds to cross a tree. What is the length of the train?

• • • • •

Convert speed into meters/ second 72*5/18 =20 meters / s Speed covered in 7 seconds = 7*20 = 140 meters. Length of train is 140 meters.

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