Question

•
Average of two numbers is 162; their H.C.F. is
12 and L.C.M. is 600. Find the number.​

Answer 1

Step-by-step explanation:

let two numbers be = a & b

sum of two numbers is = 162*2 = 324 = a+b ----------(1)

now, product of two numbers = lcm*hcf = 12*600 = 7200 = ab -------------(2)

Now, we know that

(a+b)² = (a-b)²+4ab

putting values of (1) and (2) we get ,

(324)² = (a-b)² + 4*7200

(a-b)² = (324)²-4*7200

= 76176

(a-b) = √76176 = 276 -------------(3)

solving (1) and (3) we get,

2a = 600

a = 300 & b = 24 (ans.) ✍️

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