Question 69

The product of two 2-digit numbers is 2160 and their H.C.F. is 12. The numbers are

Solution

Let the two numbers be $$12x$$ and $$12y$$ respectively where $$x$$ and $$y$$ are co-primes

Product of numbers = $$(12x) \times (12y)=2160$$

=> $$xy=\frac{2160}{144}=15$$

Possible pairs of $$x$$ and $$y$$ whose H.C.F. is 1 = $$(3,5)$$

$$\therefore$$ Required numbers = $$(12 \times 3),(12 \times 5)$$

= 36 , 60

=> Ans - (C)

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