10 june maths ii

8/14/2019 10 June Maths II

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MathsMathsDr. T.K. Jain.Dr. T.K. Jain.

AFTERSCHOOOLAFTERSCHOOOLM: 9414430763M: 9414430763

[email protected]@yahoo.co.in

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A ladder leaning against a vertical wall makesan angle of 45 degree with the ground. The

foot of the ladder is 3 meters from the wall.

What is the length of ladder? 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 Sec45 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.

A


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Answer continued:

standard values

0-10180

Infinite0190

3^1/21/23^1/2/260

1^1/2^1/2451/3^1/23^1/2/21/230

0100

TanCosSinAngle


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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.


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The pilot of a helicopter at an altitude of 1200m. finds that 2 ships are sailing towards it inthe same direction. Angles of dipression of

ships are 60 and 45 degrees. What is thedistance between ships?

Perpendicular = 1200 We have to find base.We will use Cot 45 & cot 60.Cot 45 = Base / Per =1, Base = 1200Cot 60 = Base / per = 1/3^1/2; Base =

1200/3^1/2

= 692.Distance between ships = 1200-692 = 508meters ans.

Hel


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A baloon is connected through a cable. Thelength of cable is 200 m. the baloon is inclinedat 60 degrees to the horizontal. What is the

height of baloon? 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.

B

200 m


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A,B,C,D, are 4 consecutive odd numbers. Whatmust 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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in t e c ance o t rowingless than 16 in a throw of 3

dice? Total number of possibilities in threethrows: 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 = 103/108ans.


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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 kmp.h. each. They are 400 km apart. A bird is movingfrom 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 is120 km p.h.

For bird, we will combine speed ofbird and 2nd train = 160.

400/160 = 2.5 hours. Ans.


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In the previous question, the bird returnsback 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 alsotravelled 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 tothe first train.


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If the bird keep shunting between the twotrain 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.

T i


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T e iagona s o a r om usare 24 & 10. What is the

length of its side? Apply pythogorus rule, take anyquadrant. One quadrant has one sideas 12 and other as 5. applyingpythogorus rules, we get 13 asanswer.

(12^2 +5^2) = 169

Square root of 169 is 13.

d f i i 63 k h I


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Speed of a train is 63 km per hour. Ittakes 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 = 350Platform = 350-140= 210 m.


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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 = 125/7500 =1/60

Reverse it , answer is 60 km / hour.Ans.

A l t l di t f 2500


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An aeroplane travels distances of 2500km 1200km, 500 km 400km at speedsof 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 anddownstream 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 workedfor 2 days. Then B complted remaining work in

9 days. How much time will be taken by B in

completing the entire work alone? As one days work = 1/20

2 days work = 2/20 =1/10

Remaining work = 9/10 Bs one days work = 9/10 *1/9 =1/10

Thus B will be able to complete thework in 10 days.

t t i i


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ut t ese in ascen ingorder?

3/8, 7/16, 5/12 1/6 3/8 is equal to 6/16 therefore it is smallerto 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 thenumbers,

We get 18, 21, 20, 8,

The ascending order: 1/6, 3/8, 5/12, 7/16ans.


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A:B 2:3, B:C = 5:9 A:B:C? A:B 2:3, B:C = 5:9

the ratio (using multiplyin approach). 10:15:27. ans.


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Price of Petrol 30%, how muchshould 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.

t t i t


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t o a property is wort10000. 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, hegives 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% passin 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.

I s


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In ow many ways can ewritten 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.

I s


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In ow many ways can ewritten 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 thesum of its digits. Which is the number:

36,27,45,18 45 ans.

Af h li R j d f


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Afterschooolian Raju spends ofworking time in reading, 2/3rd ofremainign time on TV. Suppose he

spends 4 hours on TV. What is hisworking time?

Remaining time

2/3 of = 6/12

Thus he spends time on TV,

Total working time with him = 8hours.

ow many num ers are


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ow many num ers arethere between 200

&300which have only one 5? There are 9 as 205, 215, 225 and soon (dont take 255).

250,251,252,253,254,256,257,258,259

Total = 18 ans.


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Divide 417 among ABCD,, A gets13>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.

Afterschooolian Rajesh takes a loan of Rs 2


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Afterschooolian Rajesh takes a loan of Rs. 2Crore and gave them as micro credit (micro

finance) @5% and gives loan to poor people at4% 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 secondsto 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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10 june maths ii

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