# SBI Clerk Mains Quantitative Aptitude (Day-61)

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Application sums

1) 6 liters are drawn from a can full of milk and is then filled with water. This operation is performed three more times. The ratio of the quantity of milk now left in can to that of the water is 81: 175. How much milk can hold originally?

A) 24 liters

B) 12 liters

C) 10 liters

D) 14 liters

E) None of these

2) Two years ago, the ratio between Raghu’s and Ravi’s salary was 17: 14. The ratio of their individual salaries between two years ago salary and this year’s salaries are 17: 25 and 7: 10 respectively. At present, the total of their salary is Rs.22500. What is the present salary of Ravi?

A) Rs.12000

B) Rs.15000

C) Rs.10000

D) Rs.14000

E) None of these

3) The population of a city was 3,20,000 three years ago. If it is increased by 5%, 1.5%, 5% respectively in the last three years, then find the present population of the city.

A) 545764

B) 358092

C) 345732

D) 435089

E) None of these

4) A boat takes 14 hours for travelling downstream from point P to Q and coming back to a point R which is at midway between P and Q. If the velocity of the stream is 8 kmph and the speed of boat in still water is 12kmph, what is the distance between P and Q?

A) 30km

B) 50km

C) 60km

D) 80km

E) None of these

5) The perimeter of a square is equal to the perimeter of a rectangle of length 28cm and breadth 42cm. Find the circumference of a semicircle whose diameter is equal to the side of the square.

A) 30cm

B) 50cm

C) 60cm

D) 90cm

E) None of these

6) Kavin covered a distance at some speed. If he had moved 6kmph faster, he would have taken 30 minutes less. If he had moved 5kmph slower, he would have taken 30 minutes more. What is the distance in km?

A) 310km

B) 320km

C) 330km

D) 340km

E) None of these

7) A boy runs opposite to that of Mumbai express at a speed of 8kmph. If the relative speed between train and the boy running in opposite direction is 30kmph. What is the length of the train, if it takes 18 seconds to cross the boy, when he is at rest?

A) 100m

B) 110m

C) 120m

D) 130m

E) None of these

8) If the numerator of a fraction is increased by 150% and denominator of the fraction is increased by ___%, the fraction becomes 4/7. The original fraction is ___. Which of the following options satisfy the given condition?

A) 150, 2/5

B) 250, 4/5

C) 100, 3/5

D) 300, 4/5

E) None of these

9) The box has 4 red balls, 3 blue balls and 2 pink balls. If three balls are drawn at random, then what is the probability of drawing exactly 2 red balls?

A) 1/14

B) 5/14

C) 3/14

D) 5/7

E) None of these

10) Geetha invests Rs.4000 in simple interest for 2 years on certain rate of interest and she gets the interest of Rs.1440. If she invests the total amount in compound interest scheme on 2% more interest rate per annum for 2 years, then find the compound interest received by Geetha?

A) Rs.2493.6

B) Rs.2393.6

C) Rs.2193.6

D) Rs.2293.6

E) None of these

Directions (1-10) :

Original quantity of milk = x liters

Quantity of milk left in can after 4 operations = [x * (1 – 6/x)4]

=>[x * (1 – 6/x)4]/x = 81/256

=> x = 24 liters

Let the salaries of Raghu and Ravi two years before be A1, B1 and now be A2, B2 respectively.

A1/B1 = 17/14 — (i)

A1/A2 = 17/25 — (ii)

B1/B2 = 7/10 — (iii)

A2 + B2 = 22500 => A2 = 22500 – B2 — (iv)

(i) * (iii) => A1/B2 = 17/20 — (v)

(ii)/(v) => B2/A2 = 4/5 — (vi)

(iv) in (vi), B2/(22500 – B2) = 4/5

=> B2 = 10000

Present salary of Ravi = Rs.10000

Required population = 320000 * (1 + 5/100) * (1 + 3/200) * (1 + 5/100)

= 358092

Downstream speed = 12 + 8 = 20kmph

Upstream speed = 12 – 8 = 4kmph

Distance between P and Q = x km

x/20 + (x/2)/4 = 14

=> x = 80km

Perimeter of square = 4a

Perimeter of rectangle = 2 * (l + b) = 2 * (28 + 42) = 140

Side of square = 140/4 = 35cm

Diameter of semicircle = 35cm

Circumference of semicircle = ∏r + 2r = 22/7 * 35/2 + 35 = 90cm

Speed = 2S1S2/(S1 – S2) = (2 * 6 * 5)/(6 – 5) = 60kmph

Distance = Speed * t1 * (1 + Speed/S1)

= 60 * 30/60 * (1 + 60/6)

= 330km

Speed of boy = 8kmph

Relative speed = Speed of train + Speed of boy

30 = Speed of train + 8

Speed of train = 22kmph

= 22 * 5/18 = 55/9 m/s

Length of train = Speed of train * Time taken to cross the boy = 55/9 * 18 = 110m

From option A,

(250/100 * 2)/(250/100 * 5) ≠ 4/7

This option does not satisfy the given condition.

From option B,

(250/100 * 4)/(350/100 * 5) = 4/7

This option satisfies the given condition.

From option C,

(250/100 * 3)/(200/100 * 5) ≠ 4/7

This option does not satisfy the given condition.

From option D,

(250/100 * 4)/(400/100 * 5) ≠ 4/7

This option does not satisfy the given condition.

Required probability = (4C2 * 5C1)/9C3

= 30/84

= 5/14

SI = P * N * R/100

1440 = 4000 * R * 2/100

R = 18%

Total amount = 4000 + 1440 = 5440

CI = P * (1 + R/100)2 – P

CI = 5440 * (1 + 20/100)2 – 5440

CI = Rs.2393.6

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