Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q1.
What is the value of  'P' , if the following equation has two equal roots ?
4x2 - (P-2)x + 1 = 0
1) P=6 or P=-2 2) P=4 or P=-3
3) P=6 or P=-3 4) P=4 or P=2
5)None of these
Answer : P=6 or P=-2
Explanation : Here, a=4,b= - (P-2); c=1
Given, equation  has equal roots,then D=0

b2- 4ac =0
or p2 +4 - 4p - 16 = 0
or p2- 6p +2p - 12 =0
or p(p-6) + 2(p-2) = 0
or p=6 or -2
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Q2.
A tank has leak which would empty the completely filled tank in 10 hours.If the tank is full of water and a tap is opened which admits 4 liters of water per minute in the tank, the leak takes 15 hours to empty the tank. How many liters of water does the tank hold ?
1) 2400 2) 3600
3) 4800 4) 7200
5)None of these
Answer : 7200
Explanation : Let, the capacity of the tank be "X" liters.
According to the problem: 15 x (X/10 - 4 x 60) = X
Or X = 7200 liters
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Q3.
The batting average of 30 innings of a cricketer is 40 runs. His highest score exceeds his lowest score by 100 runs.If these two innings are not included, the average of the remaining 28 innings is 38. What is the lowest score of the player ?
1) 12 2) 16
3) 18 4) 20
5)None of these
Answer : 18
Explanation : Let, the highest and lowest score  are x and y respectively.
So, x + y = (40 X 30 ) - (28 X 38) = 136  -------- (i)
Given, x-y = 100  -------- (ii)
Given, x-y = 100
By solving, the above equation  we get, x= 118 and x = 18
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Q4.
A vendor buy Fresh Fruits, contain 70% water and also buy Dry Fruits which contain 40% water. If he buys 120 kg of Fresh Fruits,how much quantity of Dry Fruits can be obtains from  that quantity?
1) 56 kg 2) 60 kg
3) 64 kg 4) 72 kg
5)None of these
Answer : 60 kg
Explanation : Given ,total quantity of fresh fruits = 120 kg 
In the fresh fruits , water contain = 120 x (70/100 ) = 84 kg and non-water contain = 120-84 = 36 kg.
In the Dry fruits, water contain  = 40%  and non-water contain 60%.
Since, Non-water quantity is always constant i.e. 
60% = 36 kg 
or 100% = (36/60) x 100 = 60 kg
Thus , Dry fruits quantity = 60 kg in 120 kg of Fresh fruits .

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Q5.
A shopkeeper marks up his goods by 50%. However, he could sell only one-third of his stock at this price. The half of the remaining stock was sold at a discount of 7.14% and remaining at a discount of 16.67%. What is the overall percentage profit of the trader ?
1) 28% 2) 32%
3) 36% 4) 38%
5)None of these
Answer : 38%
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Q6.
If a - b = 9 and a2 + b2 = 125, the what should be the value of ab ?
1) 16 2) 18
3) 20 4) 22
5)None of these
Answer : 22
Explanation :

First Method::

We know that, 2ab = (a2 + b2) - (a - b)2 = 125 - 81 = 44   or   ab = 22.

Second Method: 

We know that, (a - b)2 = a2 + b2 -2ab = 125- 2ab   or  81 = 125 -2ab   or  2ab = 125-81 =44 

or ab =44/2=22

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Q7.
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct ?
1) 2 p.m. on Tuesday 2) 1 p.m. on Friday
3) 3 p.m. on Thursday 4) 2 p.m. on Wednesday
5)None of these
Answer : 2 p.m. on Wednesday
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Q8.
The weights of two persons A and B are in the ratio of 4 : 5. The weight of 'A' increases by 10% and the total weight of A and B together becomes 82.8 kg, with an overall increase of 15%. By what per cent did the weight of B increase ?
1) 12.5% 2) 17.5%
3) 19% 4) 21%
5)None of these
Answer : 19%
Explanation : Allegation Method:

 10%  (C)                        x%  (D)



                  15% (M)


  (D-M) = x-15                 (M-C) = 15 -10=5

So, x-15 / 5 = 4/5
or x =15+4= 19%




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Q9.
When in each box 6 or 8 dozens of oranges were packed, five dozens were remaining. Therefore, bigger boxes were taken to pack 9 or 10 dozens of oranges. However still five dozens of oranges remains. What was the least number of dozens of oranges to be packed ?
1) 288 2) 360
3) 365 4) 435
5)None of these
Answer : 365
Explanation : LCM of 6,8,9 and 10 is 360.
So, total numbers of dozens of oranges are 360 +5 = 365
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Q10.
There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. what should be the total number of sections thus formed ?
1) 30 2) 31
3) 32 4) 35
5)None of these
Answer : 30
Explanation : HCF of 408 and 312 is 24.
So, total numbers of sections = (408+312) /24  = 30
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