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Question

27ths of a kingdom is a forest and AB fraction of the forest is a grassland. If the grassland covers 14th of the kingdom, choose the correct values of A and B

A
A = 7 ; B = 9
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B
A = 7 ; B = 8
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C
A = 14 ; B = 9
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D
A = 14 ; B = 8
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Solution

The correct option is B A = 7 ; B = 8Fraction of the kingdom covered by theforest=27 Fraction of the forest that is a grassland=AB ⟹Fraction of the kingdom that is a grassland=27×AB=2×A7×B Calculating 2×A7×B for each case, we find: Case 1:A=7 ; B=9 2×A7×B=2×77×9=2×77×9=2×11×9=29 ∴For A = 7 and B = 9, the fraction of the kingdom covered by grasslands is 29 Case 2:A=7 ; B=8 2×A7×B=2×77×8=2×77×8=1×11×4=14 ∴For A = 7 and B = 8, the fraction of the kingdom covered by grasslands is 14 Case 3:A=14 ; B=9 2×A7×B=2×147×9=2×147×9=2×21×9=49 ∴For A = 14 and B = 9, the fraction of the kingdom covered by grasslands is 49 Case 4:A=14 ; B=8 2×A7×B=2×147×8=2×147×8=1×11×2=12 ∴For A = 14 and B = 8, the fraction of the kingdom covered by grasslands is 12 Hence, the values of A and B that gives the fraction of grasslands as 14 is: A=7 ; B=8

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