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### Mathmetics

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

##### If 2x2 -7xy +3y2 = 0 ,then the value of x:y = ?
 1) 3:2 2) 2:3 3) 3:1 and 1:2 4) 5:6 5) None of these
Explanation : Given, 2x-7xy +3y= 0
or 2(x/y)2-7(x/y)+ 3 = 0
So, x/y=3/1 and x/y=1/2 View Answer
##### If a,b and c are real numbers such that  a-b+c <1 , a+b+c >1 and 9a+3b+c < -4, then what is the sign of 'a'?
 1) + only 2) - only 3) + or - 4) Can't be said 5) None of these View Answer
##### If a,b and c are the two roots of a quadratic equation such that a+b =24 and a-b = 8, the quadratic equation having a and b as its roots is ---.
 1) x2+2x+8=0 2) x2-4x+8=0 3) x2-24x+128=0 4) 2x2+8x+9=0 5) None of these
Explanation : Given, a+b =24 and a-b = 8
So,solving from two equations,we get a =16 and b=8
Therefore,ab=16 x 8 = 128
x2 - ( sum of roots)+ products of the roots = 0
or x2-24x+128 = 0 View Answer
##### 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
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 View Answer
##### 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
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 View Answer
##### 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
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 View Answer
##### 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
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 . View Answer
##### 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 View Answer
##### 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
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 View Answer
##### 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 View Answer