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11
What is the original average age of.. N. Vinaykumar Reddy Director, IACE, Hyderabad.
Model Questions 1. A and B invest some amount of money in the ratio 5:6 for same period in a business. At the end of the year, they decided to donate 25% of the profit to a temple. Out of remaining 80% was to be reinvested and the rest of the profit was divided in the ratio of their capital. If the difference in their share is Rs. 2200. Find the profit. (Approx.) a) Rs. 154000 b) Rs. 262000 c) Rs. 116000 d) Rs. 161333 e) Rs. 141542 2. A class has certain number of students and teachers. If one teacher having age of 33 years is added, the average age of the class will increase by 1 year and
Key & Solutions 1) d; Let the profit be Rs. 100. Amount left after donation = 75 Amount left after investment 75 ×
20 = 15 100
Now again, Let the amount investment = Rs X.
left
after
6X 5X − = 2200. 11 11
X = 24200. 15% of total profit = amount left after investment Total profit = 24200 ×
100 = 161333.33 15
2) c; Given, Let number of students and teachers be y and the original average age of the class be x years. So, the total age of the class = xy years. If one teacher having age of 33
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if one teacher having age of 38 years is removed, the average age of the class will decrease by 2. What is the original average age of the class? a) 28 years b) 30 years c) 24 years d) 36 years e) None of these Directions (Q.No.3-5): There are 3 bags containing 3 colored balls - Red, Green and Yellow. Bag 1 contains: 24 green balls. Red balls are 4 more than blue balls. Probability 4 of selecting 1 red ball is 13
Bag 2 contains:
7
Total balls are 8 more than 13 of balls in bag 1. Probability of selecting 1 red ball is 1/3. The ratio of green balls to blue balls is 1:2 Bag 3 contains: Red balls equal total number of green and blue balls in bag 2. Green balls equal total number of years is added, the average age of the class will increase by 1 year. So, xy + 33 = (x+1)(y+1) ⇒ xy + 33 = xy + x + y + 1 ⇒ x + y = 32 ……(i) And, if one teacher having age of 38 years is removed, the average age of the class will decrease by 2. Then, xy − 38 = (x − 2)(y − 1) ⇒ xy − 38 = xy − x − 2y + 2 ⇒ x + 2y = 40 ….(ii) Multiplying eq.(i) by 2, we get 2x + 2y = 64 ….(iii) Subtracting eq.(ii) from eq.(iii), we get 2x + 2y − x − 2y = 64 − 40 ⇒ x = 24 ∴ The original average age of the class = 24 years. 3) d; Let red = x, so blue = x −4 x
4
So (24 + x + ( x − 4)) = 13 Solve, x = 16 So bag 1: red = 16, green = 24, blue = 12 NEXT:
IBPS PO Prelims Quantitative Quantitative al i c e Aptitude Aptitude Sp
useful for
All Bank Exams
green and red balls in bag 2. Probability of selecting 1 blue 3 ball is 14
3. 1 ball each is chosen from bag 1 and bag 2, What is the probability that 1 is red and other blue? 15 128 17 c) 135 16 e) 109
21 115 25 d) 117
a)
b)
4. Some green balls are transferred bag 2: total = 8 +
7 × 52 = 36 13
green and blue = y and 2y. Let red balls = z So z + y + 2y = 36........(i) 1 Now Prob. of red = 3 z 1 So 36 = 3
Solve, z = 12 From (1), y = 8 So bag 2: red = 12, green = 8, blue = 16 NEXT: bag 3: red = 8+16 = 24, green = 12+8 = 20 Blue prob. = So
3 14
a 3 = (24 + 20 + a) 14
Solve, a = 12 So bag 3 : red = 24, green = 20, blue = 12 Now probability that 1 is red and other blue:: 16 16 12 12 25 × + × = 52 36 52 36 117
from bag 1 to bag 3. Now probability of choosing a blue ball from bag 3 becomes 3/16. Find the number of remaining balls in bag 1. a) 60 b) 58 c) 52 d) 48 e) 44 5. Green balls in ratio 4:1 from bags 1 and 3 respectively are transferred to bag 4. Also 4 and 8 red balls from bags 1 and 3 respectively. Now probability of choosing gre en ball from bag 4 is
5 . Find the 11
number of green balls in bag 4? a) 12 b) 15 c) 10 d) 9 e) 11 6. Verma has a total of Rs. 24,000. And in that, he lends Rs. 6,000 at 7/ % per annum simple interest 2 and Rs. 8,000 at 6% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of Rs. 3200 at the end of a year. The rate of interest per annum, at which the remain4) e; blue balls in bag 3 are 12 Let x green balls are transferred. So 12 3 = 56 + x 16
[56 was number of
balls in bag 3 before transfer] Solve, x = 8 So remaining number of balls in bag 1 = 52 − 8 = 44 5) c; 4x and x = 5x green balls 4 + 8 = 12 red balls So
5x 5 = 5 x + 12 11
Solve, x = 2 5 × 2 = 10 green balls 6) b; For first loan SI
PNR 6000 × 7 ×1 = × 2 = 210 100 100
For Second loan = 8000×6/100 = 480 Total interest = 3200 So, for the third loan SI =3200 − (480 + 210) = 2510 Rate of interest for third loan
ing money is lent, is (Approx.)? a) 10% b) 25% c) 15% d) 30% e) 22% Directions (Q. No. 7-11): What approximate value should come in place of question mark (?) in the following questions? 7. ?% of ( (15.85)× 25.02 + 219.85) = 224.11 a) 50 b) 45 c) 80 d) 70 e) 60 8. 2171 ÷ 14 + 24.03 × 4.97 = ? a) 175 b) 275 c) 325 d) 450 e) 225 9. ( 499 × 12.0 2) ÷ (443) + 1.992 =?2 a) 9 b) 37 c) 17 d) 13 e) 27 10. 59.98% of 599.85 × 0.801 + 92 = ? a) 144 b) 272 c) 380 d) 108 e) 94 11.
(15.88 × 7 + 52.05 + 13 × 7.01) = ?
a) 40 d) 16
b) 32 e) 8
2510 ×
c) 24
100 = 25.1% ≈ 25% 10000
7) d; ?% of ( (15.85)× 25.02 + 219.85) = 224.11 or,
? × (4 × 25 + 220) = 224 100
or, ? × 320 ≈ 224 ×100 ∴? ≈
224 × 100 = 70 320
8) b; ? = 2171 ÷ 14 + 24.03 × 4.97 ≈ 2170 ÷ 14 + 24 × 5 ≈ 155 + 120 = 275 9) c; ?2= ( 499 ×12.0 2) ÷ (443) + 1.992 ≈ (500 × 12) ÷ 21+ (2)2 ≈ 285+4 = 289 ∴ ? = √289 = 17 10) c; ? = 59.98% of 599.85 × 0.801 + 92 ≈ 60% of 600 × 0.801 + 92 ≈ 288 + 92 = 380 11) d; ? = (15.88 × 7 + 52.05 + 13 × 7.01) =
16 × 7 + 52 + 13 × 7 ≈ 256 ≈ 16
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