A) 13
B) 7
C) 14
D) 9
Correct Answer: C
Solution :
(c): Let number of bundles of oranges be \[{{B}_{1}}\]and bundle of mangoes be\[{{B}_{2}}\]. Let bundles \[{{B}_{1}}\]have n oranges and bundles \[{{B}_{2}}\]have n mangoes each. Then\[35={{B}_{1}}\times n\] and \[63={{B}_{2}}\times n\]. Since \[{{B}_{1}},{{n}_{1}},{{B}_{2}},{{n}_{2}}\]all have to be natural numbers. \[\therefore \] Possibilities are \[{{B}_{1}}=\left( 1,5,7,35 \right)\text{ }:\text{ }{{B}_{2}}=\left( 1,3,7,9,63 \right)\] Common factor is 7\[\Rightarrow \]no of fruits in each bundle = 7 \[\Rightarrow {{B}_{1}}=\frac{35}{7}=5\]and \[{{B}_{2}}=\frac{63}{7}=9\] \[\therefore {{B}_{1}}+{{B}_{2}}=14\]
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