Written Math Solution
Exam taker: #AUST
March 16, 2018
Q1: If a person invest 4000 taka at x% and 5000 taka at y%, he will get total 320 taka as interest. On the other hand if he invest 5000 at x% and 4000 at y%, he will get total 310 taka as interest. Find the value of x and y.
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Condition one:
4000*x/100+5000*y/100=320
=>40x+50y=320
=>4x+5y=32 ---------------- (1)
Condition Two:
5000*x/2+4000*y/100=310
=>50x+40y=310
=>5x+4y=31 ------------- (2)
Now, Equation (1) & (2) multiplied by 5 & 4 resoectively. We gett
20x+25y=160 ------------ (3)
20x+16y=124 ------------ (4)
________________________
(-) 9y=36
=>y=4
And, 4x+5y=32
=>4x+5*4=32
=>x=3
Answer : x & y = (3 & 4)
Q2: Working together pipe p, q & T can fill a tank in 5 hours. Working togeher o & q can fill it in 7 hours. Find in how many hours T can fill it?
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Let, Total work be 35 units (LCM of 5 & 7)
Effciency of p, q & T=35/5=7 units
Efficiency of p & q=35/7=5 units
Then, efficiency of T=7-5=2 units
So, Time taken by T=35/2
=17.5 hours (Ans.)
Q3: A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that all three are not of the same colour? (Basic Bank: Assistant Manager-2018)
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All are Not of same colour =1-All are of Same colour
All are of Same colour= (5C3+4C3+3C3)/12C3
= (10+4+1)/220
=15/220
=3/44
So, All are Not of same colour=1- 3/44
=41/44 (Ans.)
Q4: There was a shipment of cars. Out of which half was black in colour. Remaining cars were equally blue, white and red. 70% of black cars, 80% of blue cars, 30% of white cars, 40% of red cars were sold. What percentage of total cars were sold?
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Let, No. of total cars be 60
Now, Black=60/2=30
Remaining=60-30=30
So, Blue=White=Red= 30/3=10
Black sold=30*70/100=21
Blue sold=10*80/100=8
White sold=10*30/100=3
Red sold=10*40/100=4
Total sold=21+8+3+4=36
So, Required % =36*100/60
=60% (Ans.)
Note: Any suitable no. can be assumed as total.
Q5: A train passes a man in 3 seconds and another train from opposite direction pass the man 4 second,both train same lenth. how long time need to pass the train each other?
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Let, The length of each train be 12 (LCM of 3 & 4)
Now, Speed of 1st train =12/3=4 meters
And, Speed of 2nd train=12/4=3 meters.
Relative speed=4+3=7 meters
Relative length of Two train=12+12=24 meters
So, Required time=24/7
=3 (3/7) (Ans.)
Q6: A man works for certain hours.if his hourly payment increase by 20%. what percent of working hours may be reduce so that total income remain unchanged?
Method -1
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Let, his hourly pay Tk.10
And, total hour be 10 hours
So, oberall payment =10*10=Tk.100
At 20% increased, hourly pay=10*1.2=12
So, No. of hours=100/12=25/3 hrs
Now, Hour reduction=10-25/3
=5/3 hrs
So, hour reduction %=5*100/3*10=16.67% (Ans.)
Method-2
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Applying proportionality:
Wage=>A:B =5 :6
Hour=>A:B =6: 5
Now, Hour reduced =6-5=1
So, hourly reduction %=(1/6)*100
=16.67% (Ans.)
Q7: There were some books of novel and non fiction. Board discusses 3 times for any nobel and 5 times for any non fiction. During a year they discuss total 12 times. If there were 52 times, how many of them were nobel?
Method-1
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Let, number of nobel be 'x'
Then, non fiction=12-x
ATQ,
3x+5(12-x)=52
=>3x+60-5x=52
=>2x=8
So, x= 4 (Ans.)
Mrthod-2
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Let, no. of novel book be 'x'
Non-fiction books=y
Now, x+y=12 ----------------(1)
And, 3x+5y=52 ------------ (2)
Equation (1) multiplied by 5,
5x+5y=60 ---------------- (3)
3x+5y=52 ---------------- (4)
______________________
(-) 2x=8
=>x=4
So, Novel book was 4 (Ans.)
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