Mathmetics

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

Q81.
Two numbers are such that their difference, their sum and their product are in the ratio 1:7:24 respectively. What is the product of the two numbers ?
1) 12 2) 24
3) 36 4) 48
5)None of these
Answer : 48
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Q82.
The income of A,B and C together is Rs.14500 and they spend  60%,65% and 70% of their income respectively. If their savings are in the ratio 14:21:15 . What is the income of  B ?
1) Rs.4000 2) Rs.4800
3) Rs.5600 4) Rs.6000
5)None of these
Answer : Rs.6000
Explanation : We know that, income - expenditure = saving
Let, their income are 100% individually. 
So, A's saving = 100 - 60= 40% ; B's saving = 100 - 65= 35% ; C's saving = 100 - 70= 30%
But their saving ratio are 14:21:15.
Then, A's income , 40% = 14 or 100% =( 14/40) x 100 = 35
B's income , 35% = 21 or 100% =( 21/35) x 100 = 60
C's income , 30% = 15 or 100% =( 15/30) x 100 = 50
So, 35x + 60x + 50x = Rs.14500
or 145x = Rs.14500
or x = 100
Therefore income of B= 100x60 = Rs.6000.
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Q83.
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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Q84.
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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Q85.
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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Q86.
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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Q87.
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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Q88.
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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Q89.
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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Q90.
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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