SBI PO Prelims Quantitative Aptitude (Day-15)

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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) 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) 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) 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*[(r2 * (r + 300)]/1003

= > 2246.4 = P*[122 * (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) = 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) 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) x2+ 520 = 641

X2 = 641 – 520 = 121

X = 11, -11

II)y = -√144

Y = -12

X > y

10) Answer: E

I) 2x2+ 13x + 21 = 0

2x2 + 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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