Question

8. The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740.Jf
one number is 240 then what is the other number?
(a) 420 (b) 460 (c) 500 (d) 380
es 12 days to complete the work. Pranav takes 10 days to complete the same work.​

Answer 1

Answer:

Step-by-step explanation:

LCM = 28 \times HCF  

i.e. L = 28 H  

∴L + H = 1740  

=> 28H + H = 1740  

=> 29H = 1740  

=> H =174029 = 60  

∴L=28×60=1680  

Now,240×second number=1680×60=>Second number

=168060= 420  

[∵Product of two no.=LCM×HCF ]

Answer 2

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Answer:-

Given

LCM of two numbers is 28 times of their HCF.

⟶ LCM = 28HCF -- equation (1)

Sum of their LCM and HCF = 1740

⟶ LCM + HCF = 1740

⟶ 28HCF + HCF = 1740

[ From equation (1) ]

⟶ 29HCF = 1740

⟶ HCF = 1740/29

⟶ HCF = 60

Substitute the value of HCF in equation (1).

⟶ LCM = 28(60)

⟶ LCM = 1680

Also given that,

One of the numbers = 240.

So, Let the other number be x.

We know that,

Product of two numbers = HCF × LCM

⟶ (240)(x) = (60)(1680)

⟶ x = (60)(1680) / 240

⟶ x = 420