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Application Sums
1) Three pipes A, B and C can fill a cistern in 6, 12 and 18 hours respectively. If pipe A is kept open all the time and pipe B and C is opened alternatively for an hour, then find in how many hour the tank will be filled?
A) 4 2/9 hours
B) 5 8/15 hours
C) 4 7/12 hours
D) 5 3/7 hours
E) None of these
2) A, B and C started a business with investment in the ratio 4: 8: 9 respectively. After 1 year, A withdrew 50 % of his capital and B increased his capital by 30% of his investment. At the end of 2 years, they earned a profit of Rs. 159000. Find the share of B in the profit?
A) Rs. 52000
B) Rs. 63000
C) Rs. 57000
D) Rs. 69000
E) None of these
3) The difference between CI and SI on a certain amount at 12 % per annum for three years is Rs. 2246.4. Find the sum?
A) Rs. 42000
B) Rs. 35000
C) Rs. 60000
D) Rs. 40000
E) None of these
4) A box contains 5 red balls, 3 white balls, 7 black balls. If two balls are drawn out randomly, then find the probability that both balls are either red or black balls?
A) 31/105
B) 17/67
C) 4/35
D) 13/89
E) None of these
5) The sum of the present ages of the four members of a family is 118 years. 2 years ago, the ages of the four members A, B, C and D were in the ratio of 4 : 5 : 6 : 7. After how many years would A be as old as the present age of D?
A) 15 years
B) 12 years
C) 18 years
D) 10 years
E) None of these
Quadratic Equation
Directions (Q. 6 – 10): In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer as,
6)
I) x = √676 ÷ ∛2197
II)Â y2= 4
A) If x > y
B) If x = y or no relation can be established between x and y
C) If x < y
D) If x ≤ y
E) If x ≥ y
7)
I) 2x – 3y = -1
II)3x + 2y = -21
A) If x > y
B) If x ≥ y
C) If x < y
D) If x ≤ y
E) If x = y or no relation can be established between x and y
8)
I) x2– 4x – 21 = 0
II)y2– 8y +16 = 0
A) If x = y or no relation can be established between x and y
B) If x ≥ y
C) If x < y
D) If x ≤ y
E) If x > y
9)
I)Â x2+ 520 = 641
II)y = -√144
A) If x = y or no relation can be established between x and y
B) If x ≥ y
C) If x < y
D) If x ≤ y
E) If x > y
10)
I)Â 2x2+ 13x + 21 = 0
II)3y2+ 4y – 15 = 0
A) If x > y
B) If x ≥ y
C) If x < y
D) If x = y or no relation can be established between x and y
E) If x ≤ y
Answers :
Directions (1-5) :
1) Answer: A
Total units of work = 36 units (LCM of 6, 12 and 18)
A’s 1 hour work = 6 units
B’s 1 hour work = 3 units
C’s 1 hour work = 2 units
Work done by three pipes in 2 hours = 9 + 8 = 17 units
Work done in 4 hours = 17*2 = 34 units
Remaining will be done by pipe A= 2/9
Total time required= 4 2/9 hours
2) Answer: D
Ratio of shares:
A : B : C = (4*1 + 4*(50/100)) : (8*1 + 8*(130/100)*1) : (9*2)
= > 6 : 92/5 : 18
= > 15 : 46 : 45
The share of B in the profit = (46/106)*159000 = Rs. 69000
3) Answer: E
The difference between CI and SI for three years,
Diff = P*[(r2Â * (r + 300)]/1003
= > 2246.4 = P*[122Â * (12 + 300)]/1003
= > 2246.4 = P*[144*312]/(100*100*100)
= > P = [2246.4*100*100*100]/(144*312)
= > P = Rs. 50000
4) Answer: A
P(E) = n(E)/n(S)
n(S) =Â 15C2
n(E) = 5C2 or 7C2
P(E) = 5C2 or 7C2 / 15C2
P(E) = 31/105
5) Answer: A
According to the question,
4x + 5x + 6x + 7x + 2 * 4 = 118
= > 22x = 118 – 8
= > 22x = 110
= > x = 5
Present age of A = 4x + 2 = 22 years
Present age of D = 7x + 2 = 37 years
Required number of years = 37 – 22 = 15 years
Directions (6-10) :
6) Answer: E
I) x = √676 ÷ ∛2197
X = 26/13 = 2
II)Â y2= 4
y = 2, -2
X ≥ y
7) Answer: C
2x – 3y = -1 –> (1)
3x + 2y = -21 –> (2)
By solving the equation (1) and (2), we get,
X = -5, y = -3
x < y
8) Answer: A
I) x2– 4x – 21 = 0
(x – 7) (x + 3) = 0
X = 7, -3
II)y2-8y +16 = 0
(y – 4) (y – 4) = 0
Y = 4, 4
Can’t be determined
9) Answer: E
I)Â x2+ 520 = 641
X2 = 641 – 520 = 121
X = 11, -11
II)y = -√144
Y = -12
X > y
10) Answer: E
I)Â 2x2+ 13x + 21 = 0
2x2Â + 6x + 7x + 21 = 0
2x (x + 3) + 7(x + 3) = 0
(2x + 7) (x + 3) = 0
X = -7/2, -3 = -3.5, -3
II)3y2+ 4y – 15 = 0
3y2 + 9y – 5y – 15 = 0
3y (y + 3) -5(y + 3) = 0
(3y – 5) (y + 3) = 0
Y = 5/3, -3 = 1.667, -3
X ≤ y
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