If 13 + 23 . . . . . . + 103 = 3025, then the value of 23 + 43 . . . . . . + 203 is:
A. 7590
B. 5060
C. 24200
D. 12100
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \because {1^3} + {2^3} + {3^3}\,......\, + {10^3} = 3025 \cr & {\text{To find}} = {2^3} + {4^3} + {6^3}\,......\, + {20^3} = ? \cr & \Rightarrow {2^3}\left( {{1^3} + {2^3} + {3^3}\,......\, + {{10}^3}} \right) \cr & \left[ {{{\left( {\frac{{n\left( {n + 1} \right)}}{2}} \right)}^2} = {{\left( {\frac{{10\left( {11} \right)}}{2}} \right)}^2} = {{\left( {55} \right)}^2} = 3025} \right] \cr & \Rightarrow 8 \times 3025 \cr & \Rightarrow 24200 \cr} $$Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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