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The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?

a) 3 : 4
b) 2 : 3
c) 1 : 3
d) 2 : 1

Answer: d
Explanation: Let, B1 : B2 : B3 = 3x : 4x : 5x and
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
x = $$\frac{3y}{5}$$ and,
∴ 3x : 4x : 5x (putting the vale of x)
= $$\frac{{9{\text{y}}}}{5}:\frac{{{\text{12y}}}}{5}:\frac{{{\text{15y}}}}{5}$$
= 9y : 12y : 15y
5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y
Increment in first basket = 16
Increment in second basket = 8
Required ratio = $$\frac{{16}}{8}$$ = 2 : 1

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