Given: In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges.
Asked: If the total number of fruits on the basket is 61, how many guavas are there?
Let the number of apples, guavas and oranges in the basket be a, g & o respectively
In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges.
a/g = g/o
a*o = g^2
The total number of fruits on the basket is 61
a + g + o = 61
a + o = 61 - g
A) 16; g=16; a*o = 16^2= 2^8; a+ o = 45; Not possible
B) 20; g=20; a*o = 20^2= 2^4*5^2; a+o = 41; a=25;o=16; Possible
C) 25; g=25; a*o = 25^2= 5^4; a+ o = 36; Not possible
D) 28; g=28; a*o = 28^2= 2^4*7^2; a+ o = 33; Not possible
E) 30; g=30; a*o = 30^2= 2^2*3^2*5^2; a+ o = 31; Not possible
IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com