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Simplification
Directions (1 – 5): What value should come at the place of question mark in the following questions?
1) 902 * 28/11 – 96 * ³√512/3 =?   Â
A) 1944
B) 2040
C) 2140
D) 2256
E) None of these
2) √729/√? * 64 = √256/52 * 108
A) 525
B) 125
C) 625
D) 25
E) None of these
3) 8885.5 + 885.5 – 58.5 – 88.8 =? + 555.7
A) 9058
B) 9758
C) 9858
D) 9068
E) 9978
4) 8.33% of 5040 – 16.66% of 2160 =?% of 1200
A) 60
B) 20
C) 5
D) 50
E) None of these
5)  5 (5/24) – 8 (1/6) +4 (2/12) = 9 (7/12) – ?
A) 16 (1/8)
B) 16 (5/8)
C) 8 (3/8)
D) 8 (7/8)
E) None of these
Caselet
Directions (6 -10): Study the following information carefully and answer the questions given below.
A, B, C started a business. They invested amounts in the ratio of 1: 2: 3 for 3 months respectively. After this they invested in the ratio of 2: 3: 2 respectively. Investment of A for 6 months is 1600 less than that of C. After 6 months A, B, C invests 2000, 3000 and 4000 respectively for 3 months.
6) If the profit earned by A is 12000, what is the total profit by B and C?
A) 46000
B) 54000
C) 36000
D) 42000
E) None of these
7) If B invested 900 for second 3 months, the total profit ratio of A, B & C is
A) 34: 55: 70
B) 42: 55: 60
C) 48: 62: 91
D) 42: 34: 91
E) None of these
8) Â Find the total investment of A if the profit ratio of B to the total profit is 2: 5.
A) 12000
B) 16000
C) 14000
D) 18000
E) None of these
9) Â If the total profit earned by A and C is 32400, what is the amount invested by A, B, C in the second 3 months.
A) 3600
B) 3200
C) 2400
D) 2800
E) None of these
10) If A, B and C invests for next 3 months with the double amount they invested in the first 3 months, the profit ratio of A and B becomes 106/179. What is the overall amount invested by A?
A) 4600
B) 4700
C) 4800
D) 5700
E) None of these
Answers :
Directions (1-5) :
1) Answer: B
902 * 28/11 – 96 * ∛512/3 =?
82 * 28 – 32 * 8 =?
2296 – 256 =?
2040 =?
2) Answer: C
√729/√x * 64 = √256/52 * 108
27/√x * 64 = 16/25 * 108
= > x = 625
3) Answer: D
8885.5 + 885.5 – 58.5 – 88.8 = x + 555.7
= > x = 9068
4) Answer: C
8.33% of 5040 – 16.66% of 2160 = 12x
1/12 * 5040 – 1/6 * 2160 = 12x
420 – 360 = 12x
60 = 12x
x = 5
5) Answer: C
x = – 5 (5/24) + 8 (1/6) – 4 (2/12) + 9 (7/12)
x = 8 (-5 + 4 – 4 + 14)
x = 8 (9/24) = 8 (3/8)
Directions (6 – 10):
1st 3 months: x: 2x: 3x
2nd 3 months: 2y: 3y: 2y
3rd 3 months: 2000: 3000: 4000
2y + x = (2y + 3x) – 1600
x = 800
So, 1st 3 months: 800: 1600: 2400
To find profit,
(x * 3) + (2y * 3) + 6000: (2x * 3) + (3y * 3) + 9000: (3x * 3) + (2y * 3) + 12000
3x + 6y + 6000: 6x + 9y + 9000: 9x + 6y + 12000
x = 800 so,
6y + 8400: 9y + 13800: 6y + 19200
6) Answer: D
Now,
A’s profit, 6y + 8400 = 12000
y = 600
B and C’s profit, 9y + 13800 + 6y + 19200 = 5400 + 13800 + 3600 + 19200
= 42000
7) Answer: A
B: 3y = 900
y = 300
Profit ratio,
(6 * 300 + 8400): (9 * 300 + 13800): (6 * 300 + 19200)
10200: 16500: 21000
Profit ratio of A, B and C = 34: 55: 70
8) Answer: B
Given ratio = (9y + 13800)/(21y + 41400) = 2/5
45y – 42y = 82800 – 69000
3y = 13800
y = 4600
Now, 800 + (2 * 4600) + 6000 = 16000
9) Answer: D
A & C’s profit
12y + 27600 = 32400
y = 400
For second 3 months,
2y + 3y + 2y = 7y = 2800
10) Answer: A
Profit ratio of A and B,
(6y + 8400 + 1600)/(9y + 13800 + 3200) = 106/179
(6y + 10000)/(9y + 17000) = 106/179
y = 100
Overall investment by A,
x + 2y + 2000 + 2x = 800 + 200 + 2000 + 1600 = 4600
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