Aptitude - Percentage - Discussion
Discussion Forum : Percentage - General Questions (Q.No. 8)
8.
Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Answer: Option
Explanation:
| 5% of A + 4% of B = | 2 | (6% of A + 8% of B) |
| 3 |
 |
5 | A + | 4 | B | = | 2 |  |
6 | A + | 8 | B |  |
| 100 | 100 | 3 | 100 | 100 |
| |
1 | A + | 1 | B | = | 1 | A + | 4 | B |
| 20 | 25 | 25 | 75 |
| |
|
1 | - | 1 | A = |
|
4 | - | 1 | B |
| 20 | 25 | 75 | 25 |
| |
1 | A = | 1 | B |
| 100 | 75 |
| A | = | 100 | = | 4 | . |
| B | 75 | 3 |
Required ratio = 4 : 3
Video Explanation: YouTube Video
Discussion:
52 comments Page 1 of 6.
Saranya said:
1 decade ago
sum of 5% of a and 4% of b = 5/100 * a + 4/100 * b
sum of 6% of A and 8% of B = 6/100 * a + 8/100 * b
5/100 * a + 4/100 * b =2/3 (6/100 * a + 8/100 * b)
3(5/100 * a + 4/100 * b)= 2 (6/100 * a + 8/100 * b)
15a/100 + 12b/100 = 12a/100 + 16b/100
(15a+ 12b)/100 = (12a + 16b)/100 (cancel 100)
15a + 12b = 12a + 16b
15a - 12a = 16b - 12b
3a = 4b
a/b = 4/3
a:b = 4:3
sum of 6% of A and 8% of B = 6/100 * a + 8/100 * b
5/100 * a + 4/100 * b =2/3 (6/100 * a + 8/100 * b)
3(5/100 * a + 4/100 * b)= 2 (6/100 * a + 8/100 * b)
15a/100 + 12b/100 = 12a/100 + 16b/100
(15a+ 12b)/100 = (12a + 16b)/100 (cancel 100)
15a + 12b = 12a + 16b
15a - 12a = 16b - 12b
3a = 4b
a/b = 4/3
a:b = 4:3
Allana said:
1 decade ago
@Nitish
your 3rd step '3(5A + 4B) = 2(6A + 8B)' after solving this we get answer as 'C' which is 3:4...
Here is my explanation from your step 3...
3(5A + 6A) = 2(4B + 8B)
3(5A + 6A) = 3x5A = 15A and 3x6A = 18A Total = 33A i:e A = 4(Approx)
2(4B + 8B) = 2x4B = 8B and 2x8B = 16B Total = 24B i:e B = 3
Taking A/B as 33/24 we get 4/3.
your 3rd step '3(5A + 4B) = 2(6A + 8B)' after solving this we get answer as 'C' which is 3:4...
Here is my explanation from your step 3...
3(5A + 6A) = 2(4B + 8B)
3(5A + 6A) = 3x5A = 15A and 3x6A = 18A Total = 33A i:e A = 4(Approx)
2(4B + 8B) = 2x4B = 8B and 2x8B = 16B Total = 24B i:e B = 3
Taking A/B as 33/24 we get 4/3.
N!t!$h said:
1 decade ago
I would suggest , keep 100 as it is and remove it from both sides
it makes it simple
(5A/100 + 4B/100) = 2/3(6A/100 + 8B/100)
Eleminating 100 from both the side...
3(5A + 4B) = 2(6A + 8B)
solving this
3A=4B
A/B = 4/3
Done ... Keep it Simple Silly ;)
it makes it simple
(5A/100 + 4B/100) = 2/3(6A/100 + 8B/100)
Eleminating 100 from both the side...
3(5A + 4B) = 2(6A + 8B)
solving this
3A=4B
A/B = 4/3
Done ... Keep it Simple Silly ;)
(1)
UNKNOWN said:
1 year ago
Sum of both sides is a percentage initially removing the percentage than the remaining value with A and B.
5A + 4B = 2/3(6A+8B).
15A + 12B = 12A + 16B.
3A = 4B.
A/B = 4/3.
A:B = 4:3.
5A + 4B = 2/3(6A+8B).
15A + 12B = 12A + 16B.
3A = 4B.
A/B = 4/3.
A:B = 4:3.
(93)
Vana said:
10 years ago
Please why are we multiplying 2/3 by the both sides of the equation, like why the 3 in the left hand side and the 2 in the right hand side? I have never seen someone doing this?
Vinod Anand said:
1 decade ago
According to Question is :
5xA/100 + 4xB/100 = 2/3(6xA/100 + 8xB/100).
5A+4B = 2/3(6A+8B).
15A + 12B = 12A + 16 B.
3A = 4 B.
A:B = 4:3 , Option (D).
5xA/100 + 4xB/100 = 2/3(6xA/100 + 8xB/100).
5A+4B = 2/3(6A+8B).
15A + 12B = 12A + 16 B.
3A = 4 B.
A:B = 4:3 , Option (D).
Breejesh said:
1 decade ago
@Nitiesh and @Allana.
I don't understand how 3a=4b that becomes a/b=4/3.
To me 3 is with a and 4 is with b so should not be it as 3:4.
Why answer is 4:3.
I don't understand how 3a=4b that becomes a/b=4/3.
To me 3 is with a and 4 is with b so should not be it as 3:4.
Why answer is 4:3.
Amrit said:
10 years ago
Mohit if 4B = 3A then we can consider 4*B = 3*A and now when you will simplify it as A/B will become A/B = 4/3 it means the ratio is A:B = 4:3.
(1)
Rama krishna mahapatra said:
1 decade ago
Let us take x = 2 and y = 3.
If we find x/y,
Then we write x/y = 2/3.
Similarly here x/y = 4/3.
Here x = 4 and y = 3.
=>x:y = 4:3.
If we find x/y,
Then we write x/y = 2/3.
Similarly here x/y = 4/3.
Here x = 4 and y = 3.
=>x:y = 4:3.
Mazher said:
10 years ago
Can anyone tell me why we take 2/3 and multiply 3 in the left and the 2 in the right?
That's the first time seeing this property?
That's the first time seeing this property?
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