Mathmetics

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

Q111.
In a school, 3/7 of the students are girls and the rest are boys. 1/4 of the boys are below ten years of the age and 5/6 of the girls are also below ten years of age. If number of students above ten years of age is 500 , find the total number of students in the school ?
1) 1000 2) 1200
3) 1400 4) 2000
5)None of these
Answer : 1000
Explanation : Let, total numbers of students are x.
Girls = 3x/7. and boys = 1 - 3x/7 = 4x/7.
Below 10 years boys = (4x/7) 1/4 = 4x/28 = x/7
The girls are also below ten years of age = (3x/7) 5/6 = 5x/14
So, above ten years = x - (x/7 + 5x/14) = x- x/2 = x/2 
Given, x/2= 500 
or x = 1000.

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Q112.
A vendor sells 20 articles and gets a profit which is equal to cost price of 4 articles. What is his percentage of profit in this transaction ?
1) 20 % 2) 24 %
3) 25 % 4) 33.33 %
5)None of these
Answer : 20 %
Explanation :  Let, C.P of each article is Rs.1/.
So, C.P of 20's articles = Rs.20/ and C.P of 4's articles = Rs.4/  i.e. profit 
We know that,  S.P = C.P + Profit = 20 + 4 = Rs. 24/ 
Therefore, % of profit = (4/20) x 100 = 20%
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Q113.
A vendor sells 20 articles and gets a profit which is equal to selling price of 4 articles. What is the percentage of profit in this transaction ?
1) 20 % 2) 24 %
3) 25 % 4) 33.33 %
5)None of these
Answer : 25 %
Explanation : Let, S.P of each article is Rs.1/.
So, S.P of 20's articles = Rs.20/ and S.P of 4's articles = Rs.4/ i.e. profit 
We, know that C.P = S.P -Profit = 20 - 4 = Rs. 16/ 
Therefore, % of profit = (4/16) x 100 = 25%
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Q114.
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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Q115.
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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Q116.
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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Q117.
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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Q118.
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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Q119.
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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Q120.
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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