CAT 2017 – Slot 1 – Quantitative Ability – Arun's present age in years is 40% of Barun's

Q. 1: Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period?

Correct Answer:- 20

Explanation:- Let Barun’s age be 10x. Arun’s age is 4x. The difference of these ages in 6x, a constant. When Arun’s age is 50% of Barun’s age, this difference also would be 50% ie Barun’s age, at that stage would be 12x. It would be increase by 20%.

 

Q. 2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

 we can see that,

On Day 1, the person works alone. So, work done on Day 1 = 1/120

Next day, another person joins him, Work done on Day 2 = 2/120

And so on, until the final day

So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1

(1/120) (1 + 2+3+……+n) = 1

(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)

On solving, we get n = 15.

Q. 3: An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

 we can see that,

53 + …….. + 57 = 630

Remaining sum of weights = 630 – 53 – 57 = 520

Now, the minimum weight can be 53. So, to find maximum number of people

N(max) = 520/53 = 9.81

So, maximum number of people possible = 9+2 = 11

Answer: 11

 

Q. 4: A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is

 we can see that,

Speed in first case: s

Speed in second case: s’ = 5s/4

We know that, time is inversely proportional with speed

Therefore, the time would be 4/5 times the time, i.e., 1/5 less. This one fifth is 20 min. Therefore, the time taken in the first case is 100 min.

The distance = 12*(5/3) = 20 km

Answer: 2

Q. 5: Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi’s savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi’s total monthly savings (in Rs) is

we can assume that,

Total amount of savings as ‘s’

Amount kept in FD = 0.5s

Savings left = 0.5s

Amount kept in stocks = (0.3) * (0.5) * s = 0.15s

Amount kept in Bank Account = (0.7) * (0.5) * s = 0.35s

Amount deposited in the bank = 0.5s + 0.35s = 0.85s = 59500. So, s = 70000.

Answer: 70000

Checkout Other Questions of CAT 2017 Slot 1 Paper:

Verbal Ability :              |   Q.01- Q.06  |  Q.07- Q.12  |  Q.13- Q.18  |  Q.19- Q.21  |  Q.22- Q.24  |  Q.25- Q.29  |  Q.30 – Q.34  |

Logical Reasoning :    |   Q.01- Q.04  |  Q.05- Q.08  |  Q.09- Q.12  |  Q.13- Q.16  |  Q.17- Q.20  |  Q.21- Q.24  |  Q.25 – Q.28  |   Q.29 – Q.32  |

Quantitative Aptitude: |   Q.01- Q.05  |   Q.06- Q.10Q.11- Q.15  |  Q.16- Q.20  |  Q.21- Q.25  |   Q.26- Q.30  |  Q.31 – Q.34  |

 

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