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syed

· started a discussion

· 1 Months ago

query (Question: 117748.0 )

describe the solution

Question:
LCM of two number is 14 times their HCF. The sum of the LCM and the HCF is 600. If one number is 280, then the other number is:
Options:
A) 40
B) 60
C) 80
D) 100
E) 90
Solution:
Ans: (c)


Let the LCM of the numbers be Y , the HCF of the numbers be X, the numbers be P and Q where, P=280.


Y=14X .....(1) (Given)


X+Y=600 .....(2) (Given)


Subsittuting (1) in (2),


X+14X=600 


=> 15X=600 


=> X=40


Y=14(40) 


=> Y=560


Now,


X(Y)=P(Q) 


=> 560(40)=280Q 


=> Q=560(40)/280


On Solving further,


Q=80


So, the other number is 80.


kanhaiya jha

· commented

· 1 Months ago

:)

syed

· commented

· 1 Months ago

thank you

kanhaiya jha

· commented

· 1 Months ago

Let the LCM of the numbers be Y , the HCF of the numbers be X, the numbers be P and Q where, P=280.

Y=14X .....(1) (Given)

X+Y=600 .....(2) (Given)

Subsittuting (1) in (2),

X+14X=600

=> 15X=600

=> X=40

Y=14(40)

=> Y=560

Now,

X(Y)=P(Q)

=> 560(40)=280Q

=> Q=560(40)/280

On Solving further,

Q=80

So, the other number is 80.
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