A) 2280
B) 2260
C) 2420
D) 2340
E) 2380
Correct Answer: D
Solution :
Let the numbers be 6x and 6y where x and y are co-primes. According to the question, \[6x-6y=18\] \[\Rightarrow 6\left( x-y \right)=18\] \[\Rightarrow x-y=3~\] ..... (i) Product of numbers = HCF \[\times ~\]LCM \[\Rightarrow \,6x\times 6y=6\times 168\] \[\Rightarrow xy=\frac{168}{6}=28\] ??. (ii) On squaring equation (i), \[{{(x-y)}^{2}}={{3}^{2}}\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}-2xy=9\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}-2\times 28=9\] \[\Rightarrow \,\,{{x}^{2}}+{{y}^{2}}=9+56=65\] \[\therefore \,\,36{{x}^{2}}+36{{y}^{2}}=36\times 65=2340\]
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