Quantitative Aptitude Word Problems | IBPS PO (18 – 09 – 2017)

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Quantitative Aptitude Word Problems | IBPS PO (18 – 09 – 2017)
1. A right angled triangle, whose perpendicular sides measure 1.8 cm and 2.4 cm, is inscribed in a circle. What is the circumference of the circle (in cm)?
a) 1
b) π
c) 2π
d) 3π
e) 4π
2. There are 52 beggars outside the temple. 312 apples are distributed among them so that each man gets 9 apples and each woman gets 5 apples. Find the number of men and women outside the temple.
a) 13, 39
b) 39, 13
c) 14, 38
d) 26, 26
e) 38, 14
3. A box contains 21 balls numbered 1 to 21. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls are even numbered?
a) 2/7
b) 8/21
c) 3/14
d) 5/21
e) None of these
4. A sum of ₹ 13360 was borrowed at 35/4% per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment?
a) Rs.5769
b) Rs.7569
c) Rs.7009
d) Rs.7500
e) Rs.7609
5. Hardik and Pandya sold their bats at Rs. 5457 each but Hardik incurred a loss of 15%, while Pandya gained 2%. What is the ratio of the cost price of the bat of Hardik to that of Pandya?
a) 101 : 90
b) 467 : 389
c) 738 : 797
d) 642 : 537
e) None of these
6. The marks scored by Ramnath in three subjects are in the ratio 3 : 5 : 6. Ramnath scored an overall aggregate of 70% in the exam. If the maximum marks in each subject are the same, in how many subjects did Ramnath score more than 75% marks?
a) One
b) Two
c) Zero
d) Can’t be determined
e) None of these
7. Ady is a working and Sandy is a sleeping partner in a business. Ady puts in Rs. 20000 and Sandy puts in Rs. 30000. Ady receives 15% of the profit for managing the business, and the rest is divided in proportion to their capitals. If the total profit is Rs. 10500, then find the share of Sandy in the profit.
a) Rs.5355
b) Rs.3570
c) Rs.5000
d) Rs.5400
e) Rs.5300
8. A driver of an auto rickshaw sees a lorry 60 meters ahead of him. After 30 seconds the lorry is 90 meters behind. If the speed of the auto rickshaw is 38 kmph, then what is the speed of the lorry?
a) 23 kmph
b) 25 kmph
c) 20 kmph
d) 18 kmph
e) 22 kmph
9. The price of rice has increased by 20%. Lalu has decided to spend only 8% more than what he initially did on buying rice. What is the percentage decrease in Lalu's rice consumption?
a) 10%
b) 13%
c) 18%
d) 14%
e) 12%
10. The sum of the ages of Kidambi and Srikanth 14 years hence will be equal to 2 times their present age. If at present Kidambi is 8 years elder to Srikanth, then what are their present ages?
a) 22, 8
b) 29, 12
c) 18, 10
d) 13, 6
e) 15, 7
11. Parvati deposited ₹ 5,000 at a newly opended branch of Bharitya Mahila Bank at 10% rate of interest for 2 years presuming the interest to be calculated on the principal sum only once a year. How much more money will Parvati have in her account at the end of two years, if the interest is compounded semi-annually?
a) Rs.50
b) Rs.40
c) Rs.77.50
d) Rs.85.50
e) None of these
12. Boman had a certain amount with him. He spent 20% of that to buy a new cellphone and 15% of the remaining on buying a laptop. Then he donated ₹ 160 in a temple. If he is left with ₹ 1,200, how much did he buy the laptop for:
a) 220
b) 240
c) 320
d) 350
e) 360
13. The speed of a boat in still water is 16 km/h and the speed of the current is 2 km/h. The distance travelled by the boat from point A to point B downstream is 12 km more than the distance covered by the same boat from point B to point C upstream in the same time. How much time will the boat take to travel from C to B downstream?
a) 3 hrs
b) 2 hrs 30 min
c) 3 hrs 20 min
d) 2 hrs 20 min
e) 3 hrs 30 min
14. A retailer instead of raising the marked price reduced the cost price by 20% while stitching the price tag on its product. Further the company offers a discount of 6.25% to its customers. In the process company incurs a loss of Rs. 42.5 on a single article. What is the SP of that article?
a) 123.5
b) 127.5
c) 135
d) 140
e) 135
15. Three small businessmen Atal, Bihari and Vajpayee started working on an idea together. They invested ₹ 45000, ₹ 60000 and ₹ 90000 respectively in the beginning. After 3 months, Bihari took out ₹ 20000 and Vajpayee took out ₹ 60000. They got a profit of ₹ 12750 at the end of the year. Bihari’s share in the profit is:
a) Rs.5225
b) Rs.5250
c) Rs.4250
d) Rs.4520
e) Rs.4500

Solutions:
1. D) As the angle in a semicircle is always a right angle, any right angled triangle with all three of its points on the circumference of a circle must have its hypotenuse as the diameter.
To find the diameter, we just need to find the hypotenuse using the Pythogoras theorem.
  Hypotenuse =     √(1.82 + 2.42) = 3 cm
  The circumference of the circle = πD = 3π cm

2. A) Let the no. of men be x and women be y.
Now, as per the question
x + y = 52     ...(i)
9x + 5y = 312      ...(ii)
After solving eqn. (i) and (ii), we get
x = 13 (Men), y = 39 (Women)

3. C) There are 10 even numbers in the group 1-21.
   The probability that the first ball is even numbered = 10/21
Since the ball is not replaced there are now 20 balls left, of which 9 are even numbered.
The probability that the second ball is even numbered = 9/20
   Required probability = 10/21 × 9/20 = 9/42 = 3/14

4. B)


5. E) CP of Hardik's bat = 5457/85 × 100 = 321 × 20 = Rs.6420
CP of Pandya's bat = 5457/102 × 100 = 107 × 50 = Rs.5350
   Ratio = 6420 : 5350 = 642 : 535 = 6 : 5

6. A) Let the maximum marks in each subject be 100. 
  Ramnath’s total score = 70% of (100 + 100 + 100) = 70% of (300) = 210 
Also, 75% marks in a subject correspond to 75% of (100) = 75 
Let Ramnath have scored 4x, 5x and 6x in the three subjects.
  3x + 5x + 6x = 210
  14x = 210 i.e. x = 15
Hence, his marks in the three subjects are 45, 75 and 90 . 
Hence, he has scored more than 75 in exactly one subject.

7. A) The amount which Ady receives for managing the business = 15/100 × 10500 = 1575
Remaining amount of profit = 10500 – 1575 = Rs. 8925
The rest of the profit is to be divided in the ratio 2 : 3.
   Sandy's share in the profit = 8925 × 3/5 = Rs.5355

8. C) Relative Speed is (Total distance/Total Time) = (60 + 90)/30 = 5 m/s
5 m/s = 5 × 18/5 = 18 kmph
Now relative speed = speed of auto rickshaw – speed of lorry
or, 18 = 38 – speed of lorry
   Speed of lorry = 38 18 = 20 km/h

9. A) Let the initial price of Lalu be Rs. 100 per unit and Lalu's consumption be 10 units.
   Initial amount spent = 100 × 10 = 1,000
New price of rice = 120% of 100 = ₹ 120 and new total amount spent = 108% of 1000 = ₹ 1,080
   New consumption = 1080/120 = 9 units
  Decrease in consumption = 1 unit
  % decrease = 1/10 × 100 = 10%

10. C) Let the present ages of Kidambi and Srikanth be x years and y years respectively.
As per the question,
(x + 14) + (y + 14) = 2(x + y)
x + y + 28 = 2x + 2y
x + y = 28    .....(i)
Also,
y + 8 = x
x – y = 8       .....(ii)
Solving eqns (i) and (ii), we get
x = 18 and y = 10
Therefore, Present ages of Kidambi and Srikanth is 18 years and 10 years respectively.

11. A) If the interest is calculated only once a year, it must be a case of Simple Interest.
Net % rate of interest at SI for 2 years = 10 × 2 = 20%
Now, as in the 2nd scenario the sum is calculated at CI on half-yearly basis, we can find the overall rate of interest approximately by applying the net % effect formula thrice.
Net % rate for 1st two half-years = 5 + 5 + (5 × 5)/100 = 10.25%
Net % rate till next half-year = 10.25 + 5 + (10.25 × 5)/100 = 15.25 + 0.5125 ≈ 15.76%
Net % rate till the last half year = 15.76 + 5 + (15.76 × 5)/100 = 20.76 + 0.788 ≈ 21.55
   Difference in CI and SI = 21.55 ~ 20 = 1.55%
   1.55% of 5000 = 77.5

12. B) Let the Boman had total amount = ₹ 100.
Money spent on buying the cellphone = 20% of 100 = ₹ 20
Remaining amount after spending on cellphone = 100 – 20 = 80
Money spent on buying the laptop  = 15% of 80 = 12
Remaining amount after spending on laptop = 80 – 12 = 68
Now, applying the rule of proportion, we get
68  ≡ 1200 (the money left) + 160 (donated money) or
68 ≡ 1360
12 ≡ x
X = (1360 × 12)/68 = ₹ 240

13. D) Upstream speed = 16 – 2 = 14 kmph
Downstream speed = 16 + 2 = 18 kmph
Let the distance from B to C be 'd' km. Therefore the distance between A and B will be 'd+12' km.
As per the question,
Time taken to travel 'd' at 14 kmph = Time taken to travel (d + 12) at 18 kmph
Then d/14 = (d + 12)/18
or, 18d = 14d + 12 × 14
or, 4d = 12 × 14  d = 42 km
Now, the time taken by the boat to cover the distance from C to B downstream
= 42/18 hrs = 2 1/3 hrs = 2 hrs 20 min

14. B) Let the CP be x
Now CP = 80x/100
Discount price = 93.75/100 × 80/100 × x
Now, loss of the company = Original CP – Discounted (Selling) Price
Therefore, Loss = x – (93.75 × 80x)/10000 = 42.5
 10000x – 7500x = 42.5 × 10000 => x = 425000/2500 = 170
Therefore, Selling price of the article = 170 – 42.5 = 127.5

15. C) Ratio of capital = Atal's capital × Time : Bihari's capital × Time : Vajpayee's capital × Time
 45000 × 12 : (60000 × 3 + 40000 × 9) : (90000 × 3 + 30000 × 9)
= 540000 : 540000 : 540000 = 54 : 54 : 54 = 1 : 1 : 1
Sum of ratios = 1 + 1 + 1 = 3
Now, Bihari's share = 1/3 × 12750 = Rs.4250