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

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The LCM and HCF of two numbers are 660 and 10 respectively. If the sum of the numbers is 170, the what should be difference of the numbers ?
 1) 30 2) 40 3) 48 4) 50 5) None of these
Explanation : Let , two numbers are 10a and 10b ,where a and b are relatively prime numbers.
According to the question,10a X b = 660
or ab = 66 ------------- (i)
Also given, 10a + 10b  = 170
or a + b = 17 ------------------- (ii)
Solving Eqs. (i) and (ii) we get a = 11 and b = 6
So, numbers are 110 and 60.
Thus, the difference is 110 - 60 = 50

When in each box 6 or 8 dozens of oranges were packed, five dozens were remaining. Therefore, bigger boxes were taken to pack 9 or 10 dozens of oranges. However still five dozens of oranges remains. What was the least number of dozens of oranges to be packed ?
 1) 288 2) 360 3) 365 4) 435 5) None of these
Explanation : LCM of 6,8,9 and 10 is 360.
So, total numbers of dozens of oranges are 360 +5 = 365
There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. what should be the total number of sections thus formed ?
 1) 30 2) 31 3) 32 4) 35 5) None of these
Explanation : HCF of 408 and 312 is 24.
So, total numbers of sections = (408+312) /24  = 30
What are the two natural numbers whose difference is 66 and the LCM is 360 ?
 1) 90 and 24 2) 120 and 24 3) 120 and 54 4) 180 and 114 5) None of these
Answer : 90 and 24
Explanation : The factors of 360 = 2 X 2 X 2 X 3 X 3 X 5
So, two numbers are 2 X 2 X 2 X 3 =24 and 2 X 3 X 3 X 5 = 90
The sum of two numbers is 27 and their H.C.F is 3. If one of the number is lies between  13 to 16, the find the value of the other number ?
 1) 12 2) 15 3) 18 4) 24 5) None of these
Explanation : Let, two numbers are 3x and 3y respectively.
Then, 3x + 3y = 27
or 3 (x + y) = 27
or (x + y) = 27/3 = 9
So, pairs of numbers are  9 = (1,8) , (2,7) , ( 3,6) and  (4,5) .
Thus the numbers are 3 x 4 = 12 and 3 x 5 =15
What is four-digit largest number which when divided by 4, 5 , 6, 8 and 12 leaves reminder is  zero in each case ?
 1) 9936 2) 9950 3) 9960 4) 9990 5) None of these
Explanation : The L.C.M of 4, 5 , 6, 8 and 12  is 120.
The four-digit largest number is 9999.
Then, if 9999 is divided by 120, reminder is 39.
So, the require number = 9999 - 39 = 9960.
A rectangular size floor has 240 feet length and 200 feet wide. How many largest square size marbels slabs are require to pave ,so that no waste of slabs in the paving ?
 1) 24 2) 25 3) 30 4) 36 5) None of these
Explanation : The H.C.F of 240 and 200 is 40.
Area of the floor = (240 X 200) square feet and area of the slab is (40X40) square feet.
So, Numbers of slabs require = (240 X 200)/(40X40) = 30.

A worker has paid Rs.4320 if he works for all day but he has paid Rs.2520 due to some days of absent in a month.How many days he was absent ?
 1) 2 days 2) 3 days 3) 4 days 4) 5 days 5) None of these
Answer : 5 days
Explanation : The H.C.F of 4320 and 2520 is 360.
So, 4320/360 = 12 days and 2520/360 = 7 days
Thus, numbers of he absent =12-7=5 days.
The H.C.F and L.C.M of two numbers are 13 and 455 respectively. If one of the numbers lies between 75 and 125, then what is that number ?
 1) 78 2) 91 3) 104 4) 117 5) None of these
Explanation : Let, two numbers are 13x and 13y respectively.
So, 13x X 13y  = 13 X 455
or xy = 35
Then, pairs  of numbers are 35 = (1 X 35) , (5 x 7).
So, second pairs is considerable i.e. 13X5 = 65 and 13 X 7 = 91

The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then what is their difference ?
 1) 10 2) 12 3) 15 4) 20 5) None of these