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13 Apr 2020, 07:28
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D
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Difficulty:
75%
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Question Stats:
65% (03:00) correct
35%
(03:29)
wrong
based on 268
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The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. What is the strength, in percentage, of the resulting solution in vessel A ?
A. 11
B. 12
C. 13
D. 14
E. 15
Are You Up For the Challenge: 700 Level Questions
A. 11
B. 12
C. 13
D. 14
E. 15
Are You Up For the Challenge: 700 Level Questions
13 Apr 2020, 09:16
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Volume of solution in each vessels = 500ml
Salt in each vessels , in A = 10% of 500 = 50 ml
In B = 22 % of 500 = 110 ml
In C = 32% of 500 = 160 ml
When 100 ml of the solution in vessel A is transferred to vessel B, salt in B = 110 + 10% of 100 = 110 + 10 = 120 ml
% of salt in B = 120/600 = 20%
So When 100 ml of the solution in vessel B is transferred to vessel C = 160 + 20% of 100 = 160 + 20 = 180
% of salt in C = 180/600 *100 = 30 %
Now when 100 ml of the solution in vessel C is transferred to vessel A , volume of solution in A = 400+100 = 500
Salt in A = 10% of 400 + 30% of 100 = 40 + 30 = 70
% of salt in A = 70/500 *100 = 14 %
correct answer D
Salt in each vessels , in A = 10% of 500 = 50 ml
In B = 22 % of 500 = 110 ml
In C = 32% of 500 = 160 ml
When 100 ml of the solution in vessel A is transferred to vessel B, salt in B = 110 + 10% of 100 = 110 + 10 = 120 ml
% of salt in B = 120/600 = 20%
So When 100 ml of the solution in vessel B is transferred to vessel C = 160 + 20% of 100 = 160 + 20 = 180
% of salt in C = 180/600 *100 = 30 %
Now when 100 ml of the solution in vessel C is transferred to vessel A , volume of solution in A = 400+100 = 500
Salt in A = 10% of 400 + 30% of 100 = 40 + 30 = 70
% of salt in A = 70/500 *100 = 14 %
correct answer D
20 Feb 2025, 19:49
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Tricky question - math itself is not that difficult and easy to understand what do, but easy to mess up any of the multiple steps fairly easily! Let's go through it.
Firstly, let's find out how much salt is in each solution:
A = 10% of 500ml - 50g salt B = 22% of 500ml - 110g salt C = 32% of 500ml - 160g salt
Step 1: 100ml A to B
If we transfer 100ml from A to B, we are giving B 100ml that is 10% or 10g salt
so B ends up with 500ml + 100ml and 110g + 10g = 600ml and 120g salt
120/600 = 0.2 so B now has 20% salt, NOT 22%!
Step 2: 100ml B to C
If we now transfer 100ml from B to C, we are giving C 100ml that is 20% or 20g salt
so C ends up with 500ml + 100ml and 160g + 20g = 600ml and 180g salt
180/600 = 0.3 so C now has 30% salt, not 32!
Step 3: 100ml C to A
If we now transfer 100ml from C to A, we are giving A 100ml that is 30% or 30g salt
so A ends up with 400ml (NOT 500 because we gave B 100 earlier!) + 100ml and 40g (not 50 because we gave B 10 earlier) + 30g = 500ml and 70g salt
70/500 = 0.14, 14% - D
Major pitfalls on this question are, imo, making a simple math error and forgetting that when you transfer from C to A, failing to account for the already transferred solution and salt from A to B earlier.
Firstly, let's find out how much salt is in each solution:
A = 10% of 500ml - 50g salt B = 22% of 500ml - 110g salt C = 32% of 500ml - 160g salt
Step 1: 100ml A to B
If we transfer 100ml from A to B, we are giving B 100ml that is 10% or 10g salt
so B ends up with 500ml + 100ml and 110g + 10g = 600ml and 120g salt
120/600 = 0.2 so B now has 20% salt, NOT 22%!
Step 2: 100ml B to C
If we now transfer 100ml from B to C, we are giving C 100ml that is 20% or 20g salt
so C ends up with 500ml + 100ml and 160g + 20g = 600ml and 180g salt
180/600 = 0.3 so C now has 30% salt, not 32!
Step 3: 100ml C to A
If we now transfer 100ml from C to A, we are giving A 100ml that is 30% or 30g salt
so A ends up with 400ml (NOT 500 because we gave B 100 earlier!) + 100ml and 40g (not 50 because we gave B 10 earlier) + 30g = 500ml and 70g salt
70/500 = 0.14, 14% - D
Major pitfalls on this question are, imo, making a simple math error and forgetting that when you transfer from C to A, failing to account for the already transferred solution and salt from A to B earlier.
