Latest Elitmus Aptitude Question SOLUTION: The difference of two numbers is 14.their lcm and hcf are 441 and 7.find the numbers. a, 21,35 b, 35,49 c, 49,63 d, 63,77

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(#M40065698) ELITMUS Numerical Ability question Numerical Keep an EYE

The difference of two numbers is 14.their lcm and hcf are 441 and 7.find the numbers.
a, 21,35
b, 35,49
c, 49,63
d, 63,77

Asked In Elitmus Harmitha (9 years ago)

Unsolved Read Solution (29)

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Read Solution (29) :

Vinay Sipani   (9 years ago)

c) 49,63


Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=>x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49
=> option c

Is this solution Helpfull? Yes (46) | No   

Ehtesham  (9 years ago)

since n1*n2=hcf*lcm
apply this formula nd check it from solution
hcf*lcm =441*7=------( first digit is 7)so check only 49,63 after multiplying gives frist digit 7.

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Ehtesham  (9 years ago)

try to solve through option see 441*7 its first digit is 7 and in option by checking all only 49*63 has 7 at its first digit so ans is 49,63.

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Lakhi kant Roy  (8 years ago)

Let 1st no=x,2nd no=y,
A/c to qustn,x-y=14
x=14+y
we know,
HCF*LCM=n1*n2
7*441=x*y
3087=(14+y)*y
3087=14y+y^2
y^2+14y-3087=0
y^2+63y-49y-3087=0
y(y+63) -49(y+63)=0
(y-49) (y+63)=0
so,y=49,then x=y+14=49+49=63
Hence,nos are 49 and 63.

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vivek tomar  (9 years ago)

49,63 USING
7A*7B=441
7A-7B=2

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Arvind Kumar  (9 years ago)

product of two nos=LCM*HCF
therefore 441*7=49*63 through option

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MONALISHA MALIK  (9 years ago)

easy trick...check by options...
a) LCM(21,35)= 105 & HCF(21,35)=7
B) LCM(35,49)=245 & HCF(35,49)=7
C)LCM(49,63)=441 & HCF(49,63)=7
D)LCM(63,77)=693 & HCF(63,77)=7
So the answer is c.

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shubham kumar  (8 years ago)

answer is part c.
lcm*hcf= no.
441*7=7*7*7*9=49,63
63-49=14

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Ajay Thakur  (7 years ago)

step 1:- product of two numbers = LCM of numbers * HCF of numbers
= 441 * 7
= 3087

step 2:- take a look which pairs from option gives 3087 on multiplying

option (c) = 49 * 63 = 3087 (also holds the property that HCF of numbers divides it fully i.e 7 divides 49 and 63 completely).

step 3:- option (c) is the correct choice.

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Yash Dugad  (9 years ago)

The LCM is to be checked since the HCF and the difference is satisfied in all the other options.
Answer. c. 49,63

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Shivam Saluja  (9 years ago)

441/7= 63
441*7/63=441/9= 47

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Yash Puri  (9 years ago)

Ans is c
x^2-(14)x-3087=0
i will form bcoz lcm*hcf =product of numbers

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palle manasa  (9 years ago)

by checking options we get lcm 441 only for 49 nd 63

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Abhishek singh  (9 years ago)

are this level questions comes in elitmus?

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pappu kumar  (9 years ago)

by the help of option u can answer.......answer is C

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kaustubh salunke  (9 years ago)

option c is the ans.

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akshay kumar  (9 years ago)

(a+b)^2=(a-b)^2+4ab;
(a+b)^2=14^2+4*441*7; (since a*b=lcm*hcf,and a-b=14 given)
a+b=112;..................(i)
and a-b=14;............................(ii)
so add (i) and (ii) and get
a=63;
and b=49; (by putting the value of a in equation (i) get b);
answer - c;

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vijay  (9 years ago)

no = hcf*LCM
= 441*7
= 3087
NOW MULTIPLICATIN OF TWON NO EQUALLS TO THAT NO
SO 49*63=3087
ANS-C

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saurabh kumar ojha  (8 years ago)

let the numbers are x and y
according to question x-y=14
then, x=14+y

so we know x*y=HCF*LCM

(14+y)*y=441*7
y^2+14y-3067=0
y= -63, 49
y=49
x=14+y=63

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Bandana Singh  (8 years ago)

Let one number be X. Other number will be 14+X.
Since, HCF and LCM are given
X*(X+14)=HCF*LCM
X^2+14X-144*7=0
Solving the quadratic equation,
X=49
Other number 49+14=63
49,63

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veenu aggarwal  (8 years ago)

c because a*b=lcm*hcf

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vineet prakash  (8 years ago)

(c) 49,63

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Mayank Aditya  (8 years ago)

c)49,63
Let a no is x, then other is x-14.
product of numbers= hcf*lcm.
x*(x-14)=441*7

from solving
u'll find the no. r 49 and 63.

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yagyesh jha  (8 years ago)

Go through option and check only lcm of those, b'coz difference and hcf of all those options have same, only option- C has lcm as 441 . that's why option C is correct

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kumari anjana  (8 years ago)

(c)=49,63 ans

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kaushal yadav  (7 years ago)

option c is right

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jaideep sharma  (6 years ago)

c . 49,63

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ANAND KISHORE  (5 years ago)

49,63
xy*hcf=lcm
xy=63
x-y=14

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krishna bhattad  (4 years ago)

c is the answer as we know the hcf of 49 and 63 is 7 and the 441 is the bigger number so try to find a big number whose lcm can give you a number 441 so answer is c

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