Mathmetics

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

Q541.
A batsman has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs, there by  increasing his average  by 5 runs. What is his average after 13th innings ?
1) 34 2) 31
3) 36 4) 32
5)None of these
Answer : 36
Explanation :
Let the batsman’s average runs up to 12th innings was x.
Total run = 12 x.
Now total run up to 13th innings = (12 x + 96)
        According to equation = (12 x + 96)/13 = x + 5  or x = 31. 
So, after 13th innings average will be 31 + 5 = 36.

Shortcut Method :
96 - (135) + 5 = 36 
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Q542.
The average salary of workers of a Factory  is Rs.6000. While the average salary of 150 technician is Rs.12000 and that of the non-technician is Rs. 3750/-. Find the total member of the Factory. 
 
1) 500 2) 600
3) 550 4) 480
5)None of these
Answer : 550
Explanation :
By alligantion method :
12000 3750

  6000
6000 - 3750 = 2250 12000 - 6000 = 6000
So, final ratio = 2250 : 6000 = 3 : 8 
So,total number of employees = (150/3) x 11 = 550
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Q543.
The average mark of 48 students in a class is 45. The average marks of the boys in the class is 40 & the average mark of the girls in the class is 50. What is the ratio between the number of boys and  girls in the class ?      
1) 3:5 2) 1:1
3) 4:5 4) D.I
5)None of these
Answer : 1:1
Explanation :
With the help of alligation method :
50      40 
  
     45  
45 - 40 = 5 50 - 45 = 5
So, final ratio = 5 : 5 = 1 : 1
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Q544.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
1) 279 2) 283
3) 308 4) 318
5)None of these
Answer : 308
Explanation : We know that H.C.F x L.C.M = Product of two numbers
So,other number = (11 x 7700)/275 = 308.
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Q545.
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
1) 1677 2) 1683
3) 2523 4) 3363
5)None of these
Answer : 1683
Explanation :
        L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
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Q546.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30  ?
1) 196 2) 630
3) 1260 4) 2520
5)None of these
Answer : 630
Explanation :
        L.C.M. of 12, 18, 21 30 = 1260.      
    Required number = (1260 ÷ 2) = 630.

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Q547.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
1) 1 2) 2
3) 3 4) 4
5)None of these
Answer : 2
Explanation :
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 x 1, 13 x 12) and 
(13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
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Q548.
 The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
1) 20 2) 23
3) 169 4) 400
5)None of these
Answer : 23
Explanation :
Let the numbers be x and y.
Then, xy = 120 and x2 + y= 289.
(x + y)2 = x2 + y+ 2xy = 289 + (2 x 120) = 529
x + y = 23.
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Q549.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
1) 101 2) 107
3) 111 4) 185
5)None of these
Answer : 111
Explanation :
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
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Q550.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
1) 40 2) 80
3) 120 4) 200
5)None of these
Answer : 40
Explanation :
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400      or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
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