Mathmetics

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

Q81.
A number gets reduced to its one-third when 48 is subtracted from it. What is two-thirds of that number ?
1) 24 2) 36
3) 48 4) 72
5)None of these
Answer : 48
Explanation : Let, the number be x.
So,x-48 = x/3
or x-x/3= 48 
or x = 72
Therefore, two-thirds of 72 is 48.
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Q82.
One third of A’s marks in Arithmetic is equal to half of his marks in English. If he gets 150 marks in the two subjects together, how many marks has he got in English?
1) 30 2) 40
3) 50 4) 60
5)None of these
Answer : 60
Explanation : Given, A’s marks in Arithmetic is x and A’s marks in English y and x +y=150 ----- (I)
so, x/3 = y/2
or 2x =3y 
or 2x - 3y = 0 ------- (II)
Putting the value in both equation, we get y = 60.


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Q83.
What is the sum of the following expression (13 + 23+ 33 + 43+ 53 + 63 + …….. + 103).
1) 2525 2) 2925
3) 3025 4) 3225
5)None of these
Answer : 3025
Explanation : We know that , the sum of the cube all natural number i.e. 1- n = [(n. n+1)/2]2

The sequence is  (13 + 23+ 33 + 43+  …….. + 103)

So, [(10 x 11)/2]2 = 3025 
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Q84.
What is value of the given sequence (53 + 63 + 73+…….. + 103) ?
1) 2295 2) 2425
3) 2595 4) 2925
5)None of these
Answer : 2925
Explanation : We know that , the sum of the cube all natural number i.e. 1- n = [(n. n+1)/2]2

The sequence is  (13 + 23+ 33 + 43+  …….. + 103) -  (13 + 23+ 33 + 43)

So, [(10 x 11)/2]2 - [(4x5)/2]2 = 3025 -100 = 2925

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Q85.
The sum of the squares of two numbers is 68 and the square of their difference is 36. what is the product of the two numbers ?
1) 16 2) 52
3) 58 4) 104
5)None of these
Answer : 52
Explanation : Let, two  numbers are x and y respectively. 
So, x2 + y2 = 68 and ( x - y )2 = 36.
We know that, ( x - y )2 = x2 + y2 - 2xy  
or 68 - 2xy = 36
or 2xy = 68+36 = 104
or xy = 104/2=52

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Q86.
If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, then what is the number ? 
1) 2 2) 3
3) 4 4) 5
5)None of these
Answer : 3
Explanation : Let, the number be x.
2x + 20 = 8x - 4
or 8x - 2x  = 20 + 4 = 24
or 6x =24
or x= 24/6= 4
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Q87.
Three-fourth of two-third of 240 is added to two-third of a number, the resultant number is 360. What is value of the original number ?
1) 180 2) 240
3) 320 4) 360
5)None of these
Answer : 360
Explanation : Given , 3/4 x 2/3 x 240 +2x/3 = 360
or 120 + 2x/3 = 360
or x = 360
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Q88.
The difference between simple interest and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. What is The sum (in Rs.) ?
1) 625 2) 630
3) 640 4) 650
5)None of these
Answer : 625
Explanation : Short -Cut Method:

Difference X (100)2/ R


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Q89.
A motorboat went down the river for 14 km and then up the river for 9 km. It took a total of 5 hours for the entire journey. What is the speed of the river flow if the speed of the boat in still water is 5 km/hr ?
1) 1 km/hr. 2) 1.5 km/hr.
3) 2 km/hr. 4) 3 km/hr.
5)None of these
Answer : 1.5 km/hr.
Explanation :
Let, the speed of the stream be x km/hr.
Then, upward speed =(5- x)km/hr.
downward speed = (5 + x) km/hr.
So, (15/5+x) + (9/5-x) = 5
or x = 2 km/hr
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Q90.
A motorboat whose speed in still water is 10 km/h went 91 km downstream and then returned to its starting point. What is the speed of the river flow if the round trip took a total of 20 hours ?
1) 3 km/hr. 2) 4 km/hr.
3) 6 km/hr. 4) 8 km/hr
5)None of these
Answer : 3 km/hr.
Explanation :
Let, the speed of the stream be x km/hr.
Then, (91/10-x) + (91/10+x) = 20
or x = 3 km./hr
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