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 = 8 Fraction 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:
Case1: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
Case2: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
Case3: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
Case4: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: