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Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of

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Bunuel
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Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink] New post   27 Mar 2020, 03:34
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Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of their salaries respectively, then their savings are in the ratio of 10:12:33. What is the C's salary?

A. 80
B. 150
C. 180
D. 210
E. 220


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B
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Re: Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink] New post   27 Mar 2020, 03:48
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Bunuel wrote:
Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of their salaries respectively, then their savings are in the ratio of 10:12:33. What is the C's salary?

A. 80
B. 150
C. 180
D. 210
E. 220


Let the salaries of A, B & C be $a, $b & $c respectively
--> a + b + c = 350 ....... (1)

If they spend 75%, 80% and 56% of their salaries respectively, then their savings are in the ratio of 10:12:33
--> 0.25a : 0.20b : 0.44c = 10 : 12 : 33
--> 0.25a = 10k; 0.2b = 12k; 0.44c = 33k; for some positive value 'k'
--> (a, b, c) = (40k, 60k, 75k)

From (1), 40k + 60k + 75k = 350
--> 175k = 350
--> k = 2

Salary of C = 75*k = 75*2 = $150

Option B
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Re: Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink] New post   27 Mar 2020, 04:27
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Bunuel wrote:
Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of their salaries respectively, then their savings are in the ratio of 10:12:33. What is the C's salary?

A. 80
B. 150
C. 180
D. 210
E. 220

Are You Up For the Challenge: 700 Level Questions

Solution:


    • Let A, B, and C be the salary of A, B, and C, respectively.
      o \(A + B + C = 350\)
    • A’s saving =\(A – \frac{75}{100}*A\) = \(\frac{25}{100}*A\)
    • B’s saving = \(B – \frac{80}{100}*B = \frac{20}{100}*B\)
    • C’s saving = \(C – \frac{56}{100}*C = \frac{44}{100}*C\)
The ratio of savings is given to be 10: 12: 33
    • \(\frac{25A}{20B} = \frac{10}{12}\)
      o \(\frac{A}{B} =\frac{2}{3}\)
      o \(A: B = 2: 3\)…(i)
    • \(\frac{20B}{44C} =\frac{12}{33}\)
      o \(B:C= 4:5\)…(ii)
On multiplying equation (i) by 4 and equation (ii) by 3, we get
    • \(A: B: C = 8: 12: 15\)
Let 8x, 12x, and 15x be the salary of A, B, and C, respectively.
    • \(8x+12x+15x = 350\)
    • \(35x = 350\)
    • \(x =10\)
      o C’s salary = \(15*10 = 150\)
Hence, the correct answer is Option B.­
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Re: Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink] New post   27 Mar 2020, 05:05
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Alternatively,

We are given that if A, B, and C spend 75%, 80%, and 56% of their salaries respectively, then their savings are in the ration 10:12:33 respectively for A, B, and C.

Focusing on C alone, after spending 56%, his savings is 44%
but the savings of A, B, and C in the ratio 10:12:33, means that their actual savings in monetary terms are 10k, 12k, and 33k respectively, where k is a positive integer.
so C's savings is 33k.
Now 44% of C=33k
Hence 44C/100=33k
11C/25 = 33k
C=25*3k = 75k

Look through the answer choices and choose the option that is a multiple 75, and luckily, only B, 150, is a multiple of 75.

The answer is B.
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Re: Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink] New post   03 Jun 2020, 01:33
Let salaries are in ratio=>
a:b:c, Total is 350
They are spending 75%, 80%, 56% respectively.

Then savings:
0.25a:0.2b:0.44c = 10:12:33
25a:20b:44c = 10:12:33

25a = 10=> a = 2/5
20b = 12 => b = 3/5
44c = 33 => c = 3/4

(2/5+3/5+3/4)x = 350
7x/4 = 350
x = 200

C = 3/4 x = 150

B
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Re: Total salary of A, B and C is $350. If they spend 75%, 80% and 56% of [#permalink]
03 Jun 2020, 01:33
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