Ratio and Proportion Query

[alaynaik]

Hello Guys,
I request you help me with the following query:

Q: A certain amount was to be divided between A,B & C in the ratio of 4:5:6 but by mistake, it was divided in such a way that 4 times A's share was equal to 5 times B's share and 6 times C's share. As a result, 'A' got $154 more than the expected amount. What was the amount that was divided among them?
a)$370
b)$450
c)$560
d)$1000
e)$1110

I request you to help me with the query.

Thanks.

[gmatboost]

We know 4A = 5B = 6C
We need to figure out what ratio this implies for A:B:C

The easiest way is to set 4A = 5B = 6C = 60 (chosen because it is the LCM of 4, 5, 6)
Then, A = 15, B = 12, C = 10
Any other number would be fine, 60 was easiest to work with
So, A:B:C is 15:12:10
A gets 15/(15+12+10) of the money = 15/37.

A was supposed to get 4/(4+5+6) of the money = 4/15

So, (15/37)x - (4/15)x = 154, where x is the total amount of money
Use a common denominator of 15*37 on the left:

(15*15)/(15*37)x - (37*4)/(37*15)x = 154
225x/(15*37) - 148x/(15*37) = 154
(225x-148x)/(15*37) = 154
(77x)/(15*37) = 154 -> Recognize that both 77 and 154 are divisible by 77
x/(15*37) = 2
[spoiler]x = 15*37*2 = 30*37 = 1110[/spoiler]

[alaynaik]

Mr.Greg Michnikov
Thanks a lot for the help...
I appreciate the efforts you put in for addressing the query...
Regards,
Alay S. Naik

[GMATGuruNY]

Hello Guys,
I request you help me with the following query:

Q: A certain amount was to be divided between A,B & C in the ratio of 4:5:6 but by mistake, it was divided in such a way that 4 times A's share was equal to 5 times B's share and 6 times C's share. As a result, 'A' got $154 more than the expected amount. What was the amount that was divided among them?
a)$370
b)$450
c)$560
d)$1000
e)$1110

I request you to help me with the query.

Thanks.

We can plug in the answers, which represent the total amount.
Since the intended ratio was 4:5:6, and 4+5+6 = 15, the correct answer must be a multiple of 15.
Eliminate A, C and D.
Answer choice B seems way too small, given that A's amount is to be increased by 154, which is more than 1/3 of 450.

Answer choice E: 1110

The determine the values for A, B and C, use a ratio box:

...............................A.........B.........C........Total

Ratio.....................4..........5..........6........15

Multiplier

Actual....................................................1110


The multiplier for the box = 1110/15 = 74. Insert the multiplier and complete the box:

...............................A.........B.........C........Total

Ratio.....................4..........5..........6........15

Multiplier..........74........74.......74......74

Actual..............296......370.....444....1110


The bottom row of the box shows the intended values for A, B and C.
Now check the altered values for A, B and C:
Increased by 154, new A = 296+154 = 450.
Thus, 4A = 4*450 = 1800.
Since 4A = 5B, new B = 1800/5 = 360.
Since 4A = 6C, new C = 1800/6 = 300.
New A + new B + new C = 450+360+300 = 1110. Success!

The correct answer is E.

[saketk]

As per the ques:-- A:B:C = 4:5:6. Let the total amount be X.
=> A's share -- 4x/15
B's share -- 5x/15
C's share -- 6x/15.

Also as per the condition given, 4A = 5B= 6C (LET THIS BE EQUAL TO P) -- equation 1
This gives, A = P/4 --- equation 2
Also, A+B+C = X ( total amount).
using equation 1, we get =

p [ (1/4) + (1/5) +(1/6)] = x

or, P = (37/60)X.

Using equation 2. we get A= 15x/37.

As per the question, final value of A - initial value = 154.

or, 15x/37- 4x/15 = 154.

Solve this (remember --Keep the RHS as it is for easy cancellation of numerator and denominator)

We will get X.

HENCE, Ans is option E