CAT 2017 Quant Question: Percentages
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? (TITA)
Answer:
Given that Arun’s present age in years is 40% of Barun’s. And after few years, Arun’s age will be half of Barun’s. We have to find by what percentage will Barun’s age increase during this period.
So Arun’s present age is 2x and Barun’s present age will be equal to 5x.
2(2x + y) = 5x + y
4x + 2y = 5x + y
4x + 2y = 5x + y
y = x
So 2x and 5x becomes 3x and 6x respectively.
By what percentage will Barun’s age increase during this period is that x increases of 5x so it increases by 20%.
Hence 20% of Barun’s age will increase during this period.
Hence, the answer is 20
CAT 2017 Quant Question: Pipes & Cisterns
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? (TITA)
Answer:
Given that 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.
Everyday a new person with the same efficiency joins the work
So by first day 1 person
Similarly by second day 2
Third day 3 and it goes on…until it makes a total of 120
We have to find how many days are required to complete the job
So 1 + 2 + 3 + 4 … till 15 days are required to complete this Job.
This will get completed in 15 days.
Hence 15 days are required to complete the job
Hence, the answer is 15
CAT 2017 Quant Question: Averages
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? (TITA)
Answer:
Given that 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.
We have to find the maximum possible number of people in the group.
We can take one person to be 57 kg and since they have asked for the maximum possible number of people it can accommodate in the lift we can take more no. of people with lightest weight.
So, at least one guy with 57 kg.
⟹ 630 – 57 = 573
Hence, 10 + 1 = 11 people
The maximum possible number of people in the group is 11.
Hence, the answer is 11
CAT 2017 Quant Question: Speed Time Distance
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: (TITA)
Answer:
Given that 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 difference between these two times is 20 minutes
We have to find the distance (in km) from his home to the railway station.
⟹ d = 20 km
The distance (in km) from his home to the railway station is 20 km.
Important point to remember is that we don’t need to take the actual time here, we can take that difference of 10 minutes before and 10 minutes after which is equal to 20 minutes i.e. 
of an hour.
Hence, the answer is 20 km
CAT 2017 Quant Question: Percentages
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: (TITA)
Answer:
Ravi invests 50% of his monthly savings in fixed deposits i.e from the remaining 50%, 30% percent of the rest of his savings = 15% is invested in stocks.
And the rest i.e 50 – 15 = 35% 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
i.e. 50 + 35 = 85 % ⟹ 85% of total savings = 59500
We have to find the Ravi’s total monthly savings (in Rs)
⟹ Total savings = 
× 100 = Rs.70000
Ravi’s total monthly savings is 70000 Rupees.
Hence, the answer is 70000
CAT 2017 Quant Question: Profit & Loss
If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?
A. Give a discount of 5% on retail price
B. Give a discount of 2% on retail price
C. Increase the retail price by 2%
D. Sell at retail price
Answer:
Given that if a seller gives a discount of 15% on retail price, she still makes a profit of 2%.
Let us assume marked price to be x. So, selling price to be 0.85x on giving 15% discount on retail price she still makes a profit of 2%.
We have to find which of the following options ensures that she makes a profit of 20% so the discount should be much lower.
Hence by selling at retail price she makes a profit of 20%.
Hence, the answer is Sell at retail price
Choice D is the correct answer.
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CAT 2017 Quant Question: Speed Time Distance
A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:
A. √6 : √2
B. √7 : 2
C. 2√5 : 3
D. 3 : 2
Answer:
Let us take the speed of the boat and river to be ‘b’ and ‘x’ respectively and let the distance be ‘d’.
As per the condition in the question,
Hence the ratio of the original speed of the motor boat to the speed of the river is equal to √7 : 2
Hence, the answer is √7 : 2
Choice B is the correct answer.
CAT 2017 Quant Question: Ratio & Proportions
Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:
A. 438 crore
B. 435 crore
C. 348 crore
D. 345 crore
Answer:
The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2 , C4 and C5 are in the ratio 18 : 19 : 20.
Now we can simplify this and take all of them into same variable so we need to take LCM for 10 and 18 which happens to be 90.
By taking 90 as LCM we get,
C1 = 81
C2 = 90
C3 = 72
C4 = 95
C5 = 100
We have to find the total profit (in Rs) made by all five companies
C5 is 19 crores more than C1 which works out as such. i.e C1 = 81 , C5 = 100.
So to get the total profit we can add them altogether = 81 + 90 + 72 + 95 + 100 = 438
Hence Rs. 438 crore is the total profit made by all five companies.
Hence, the answer is 438 crore
Choice A is the correct answer.
CAT 2017 Quant Question: Percentages
The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:
A. 35
B. 50
C. 60
D. 65
Answer:
Given that the number of girls appearing for an admission test is twice the number of boys.
Let x be the number of boys and 2x be the number of girls.
We have to find the % of candidates who do not get admission if 30% of the girls and 45% of the boys get admission.
Those who got admission is 1.05x and those who do not get admission is 1.95x.
The percentage of candidates who do not get admission is 65%.
Hence, the answer is 65
Choice D is the correct answer.
CAT 2017 Quant Question: Ratio & Proportions
A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio:
A. 1 : 1
B. 8 : 7
C. 4 : 3
D. 6 : 5