10 June Maths II
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Transcript of 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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www.a ersc ooo . social entrepreneurship for
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