Question

Beaker A and beaker B contain methanol, ethanol and phenyl in the ratio 1:3:2 and 2:1:5 respectively Some part of the solution from beaker Aand beake* B are thoroughly mixed and put into another beake’ C. Which of the following cannot be the ratio of methanol, phenyl and ethanol in beaker C?

Answer 1

Complete Question :- Beaker A and beaker B contain methanol, ethanol and phenyl in the ratio 1:3:2 and 2:1:5 respectively . Some part of the solution from beaker A and beaker B are thoroughly mixed and put into another beaker C . Which of the following cannot be the ratio of methanol, phenyl and ethanol in beaker C ?

A) 10 : 23 : 15

B) 7 : 15 : 16

C) 6 : 13 : 13

D) 9 : 20 : 17

Solution :-

Let us assume that, x part of solution from baker A and y part of solution from baker B is mixed an put into beaker C .

So, In x part we have,

→ Quantity of Methanol = x * (1/6) = (x/6)

→ Quantity of Ethanol = x * (3/6) = (x/2)

→ Quantity of Phenyl = x * (2/6) = (x/3)

and, In y part we have,

→ Quantity of Methanol = y * (2/8) = (y/4)

→ Quantity of Ethanol = y * (1/8) = (y/8)

→ Quantity of Phenyl = y * (5/8) = (5y/8)

then,

→ Total Quantity of Methanol in beaker C = (x/6) + (y/4) = (2x + 3y)/12

→ Total Quantity of Phenyl in beaker C = (x/3) + (5y/8) = (8x + 15y)/24

→ Total Quantity of Ethanol in beaker C = (x/2) + (y/8) = (4x + y)/8

therefore,

→ Ratio of (Methanol : Phenyl : Ethanol) in beaker C = (2x + 3y)/12 : (8x + 15y)/24 : (4x + y)/8 = (4x + 6y)/24 : (8x + 15y)/24 : (12x + 3y)/24 = (4x + 6y) : (8x + 15y) : (12x + 3y)

Now, putting values of x and y in given options :-

when x = y = 1 :-

→ (4 * 1 + 6 * 1) : (8 * 1 + 15 * 1) : (12 * 1 + 3 * 1) = 10 : 23 : 15

• Option (A) is possible ratio of Methanol, Phenyl and Ethanol in beaker C .

when x = (1/4) , y = (1/15) :-

→ (1 + 2/5) : (2 + 1) : (3 + 1/5) = (7/5) : 3 : (16/5) = 7 : 15 : 16 .

• Option (B) is possible ratio of Methanol, Phenyl and Ethanol in beaker C .

when x = (1/2) , y = (1/6) :-

→ (2 + 1) : (4 + 5/2) : (6 + 1/2) = 3 : (13/2) : (13/2) = 6 : 13 : 13 .

• Option (C) is possible ratio of Methanol, Phenyl and Ethanol in beaker C .

Since first three given options are possible ratio of Methanol, Phenyl and Ethanol in beaker C .

Hence, we can conclude that, Option (D) 9 : 20 : 17 cannot be the ratio of methanol, phenyl and ethanol in beaker C .

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