The LCM of two numbers is 90 times their HCF. The sum of DCM and HCF is 1456. If one of the numbers is 160; then what is the other number?
Correct Answer: Description for Correct answer:
Let one number be x and another number be y
L.C.M. x H.C.F. = Product of two number8
90 H.C.F. x H.C.F. = xy
\( \Large 90(H.C.F)^{2} = xy \)
Now one number is let x be 160 (given)
\( \Large 90(H.C.F)^{2} = 160 \times y \) ...(i)
and 90 H.C.F. + 1 H.C.F. = 1456
91H.C.F. = 1456
\( \Large H.C.F = \frac{1456}{91} = 16\)
Another number (y) = \( \Large \frac{90(H.C.F)^{2}}{160} \)
= \( \Large \frac{90 \times 16^{2}}{160} \)
= \( \Large 9 \times 16 = 144 \)
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