Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is ________
Show Hint
- 5
- 7
- 6
- 8
The Correct Option is B
Solution and Explanation
This is a relative speed problem. When two objects move towards each other, their relative speed is the sum of their individual speeds. We can find the time taken for each meeting and count how many meetings occur within the given 80-minute timeframe.
Step 2: Key Formula or Approach:
1. Let the length of the pool be L. Calculate the speeds of Ankit (\(v_A\)) and Bipul (\(v_B\)). 2. For the first meeting, they collectively cover a distance of L. Time = Distance / Relative Speed. 3. For all subsequent meetings, they collectively cover a distance of 2L (since they each swim one length to return to their starting sides and then move towards each other again). 4. Calculate the times of each meeting and count how many fall within 80 minutes.
Step 3: Detailed Explanation:
Let the length of the pool be L units. Speed of Ankit, \( v_A = \frac{L}{10} \) units/minute. Speed of Bipul, \( v_B = \frac{L}{15} \) units/minute. They are swimming towards each other, so their relative speed is: \[ v_{rel} = v_A + v_B = \frac{L}{10} + \frac{L}{15} = \frac{3L + 2L}{30} = \frac{5L}{30} = \frac{L}{6} \text{ units/minute} \] First Meeting: To meet for the first time, they need to cover a total distance of L. \[ \text{Time for 1st meeting} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{L}{L/6} = 6 \text{ minutes} \] Subsequent Meetings: After the first meeting, for them to meet again, they must collectively swim a total distance of 2L. For example, Ankit swims to one end and turns back, while Bipul swims to the other end and turns back. \[ \text{Time between subsequent meetings} = \frac{2L}{L/6} = 12 \text{ minutes} \] Now, let's find the times at which the meetings occur:
1st meeting: 6 minutes
2nd meeting: 6 + 12 = 18 minutes
3rd meeting: 18 + 12 = 30 minutes
4th meeting: 30 + 12 = 42 minutes
5th meeting: 42 + 12 = 54 minutes
6th meeting: 54 + 12 = 66 minutes
7th meeting: 66 + 12 = 78 minutes
8th meeting: 78 + 12 = 90 minutes (This is after the 80-minute duration)
Since the 7th meeting occurs at 78 minutes, which is within the 80-minute timeframe, they meet a total of 7 times.
Step 4: Final Answer:
The number of times they meet each other is 7.
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Questions Asked in IPMAT exam
- Five teams—A, B, C, D, and E—each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one speciality. The total number of biologists, geologists, and explorers are equal. The following additional information is available
• Every team has at least 2 members from each of the three skill sets.
• Teams C and D have 6 biologists each, and Team A has 6 geologists.
• Every team except A has more biologists than explorers.
• The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.- IPMAT - 2025
- Logical Reasoning
The table given below provides the details of monthly sales (in lakhs of rupees) and the value of products returned by the customers (as a percentage of sales) of an e-commerce company for three product categories for the year 2024. Net sales (in lakhs of rupees) is defined as the difference between sales (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
- IPMAT - 2025
- Data Interpretation
Meta is recalibrating content on its social media platforms as the political tide has turned in Washington, with Mark Zuckerberg announcing last week that his company plans to fire its US fact-checkers. Fact-checking evolved in response to allegations of misinformation and is being watered down in response to accusations of censorship. Social media does not have solutions to either. Community review — introduced by Elon Musk at X and planned by Zuckerberg for Facebook and Instagram — is not a significant improvement over fact-checking. Having Washington lean on foreign governments over content moderation does not benefit free speech. Yet, that is the nature of the social media beast, designed to amplify bias.
Information and misinformation continue to jostle on social media at the mercy of user discretion. Social media now has enough control over all other forms of media to broaden its reach. It is the connective tissue for mass consumption of entertainment, and alternative platforms are reworking their engagement with social media. Technologies are shaping up to drive this advantage further through synthetic content targeted precisely at its intended audience. Meta’s algorithm will now play up politics because it is the flavour of the season.
The Achilles’ Heel of social media is informed choice which could turn against misinformation. Its move away from content moderation is driven by the need to be more inclusive, yet unfiltered content can push users away from social media towards legacy forms that have better moderation systems in place. Lawmakers across the world are unlikely to give social media a free run, even if Donald Trump is working on their case. Protections have already been put in place across jurisdictions over misinformation. These may be difficult to dismantle, even if the Republicans pull US-owned social media companies further to the right.
Media consumption is, in essence, evidence-based judgement that mediums must adapt to. Content moderation, not free speech, is the adaptation mechanism. Musk and Zuckerberg are not exempt- IPMAT - 2025
- Reading Comprehension
According to the French philosopher Jean Baudrillard, commodities available for consumption are not inherently negative things. Baudrillard tried to interpret consumption in modern societies by engaging with the ’cargo myth’ prevalent among the indigenous Melanesian people living in the South Pacific. The Melanesians did not know what aeroplanes were. However,they saw that these winged entities descended from the air for white people and appeared to make them happy. They also noted that aeroplanes never descended for the Melanesian people. The Melanesian natives noted that the white people had placed objects similar to the aeroplane on the ground. They concluded that these objects were attracting the aeroplanes in the air and bringing them to the ground. Through a magical process, the aeroplanes were bringing plenty to the white people and making them happy. The Melanesian people concluded that they would need to place objects that simulated the aeroplane on the ground and attract them from the air. Baudrillard believes that the cargo myth holds an important analogy for the ways in which consumers engage with objects of consumption.
According to Baudrillard, the modern consumer ”sets in place a whole array of sham objects, of characteristic signs of happiness, and then waits for happiness to alight”. For instance, modern consumers believe that they will get happiness if they buy the latest available version of a mobile phone or automobile. However, consumption does not usually lead to happiness. While consumers should ideally be blaming their heightened expectations for their lack of happiness, they blame the commodity instead.
They feel that they should have waited for the next version of a mobile phone or automobile before buying the one they did. The version they bought is somehow inferior and therefore cannot make them happy. Baudrillard argues that consumers have replaced ’real’ happiness with ’signs’ of happiness. This results in the endless deferment of the arrival of total happiness. In Baudrillard’s words, ”in everyday practice, the blessings of consumption are not experienced as resulting from work or from a production process; they are experienced as a miracle”. Modern consumers view consumption in the same magical way as the Melanesian people viewed the aeroplanes in the cargo myth. Television commercials also present objects of consumption as miracles. As a result, commodities appear to be distanced from the social processes which lead to their production. In effect, objects of consumption are divorced from the reality which produces them.- IPMAT - 2025
- Reading Comprehension
CONVERSATION ANALYSIS: Read the following transcript and choose the answer that is closest to each of the questions that are based on the transcript.
Lucia Rahilly (Global Editorial Director, The McKinsey Podcast): Today we’re talking about the next big arenas of competition, about the industries that will matter most in the global business landscape, which you describe as arenas of competition. What do we mean when we use this term?
Chris Bradley (Director, McKinsey Global Institute): If I go back and look at the top ten companies in 2005, they were in traditional industries such as oil and gas, retail, industrials, and pharmaceuticals. The average company was worth about $250 billion. If I advance the clock forward to 2020, nine in ten of those companies have been replaced, and by companies that are eight times bigger than the old guards.
And this new batch of companies comes from these new arenas or competitive sectors. In fact, they’re so different that we have a nickname for them. If you’re a fan of Harry Potter, it’s wizards versus muggles.
Arena industries are wizardish; we found that there’s a set of industries that play by very different set of economic rules and get very different results, while the rest, the muggles (even though they run the world, finance the world, and energize the world), play by a more traditional set of economic rules.
Lucia Rahilly: Could we put a finer point on what is novel or different about the lens that you applied to determine what’s a wizard and what’s a muggle?
Chris Bradley: Wizards are defined by growth and dynamism. We looked at where value is flowing and the places where value is moving. And where is the value flowing? What we see is that this set of wizards, which represent about ten percent of industries, hog 45 percent of the growth in market cap. But there’s another dimension or axis too, which is dynamism. That is measured by a new metric we’ve come up with called the ”shuffle rate.” How much does the bottom move to the top? It turns out that in this set of wizardish industries, or arenas, the shuffle rate is much higher than it is in the traditional industry.
Lucia Rahilly: So, where are we seeing the most profit?
Chris Bradley: The economic profit, which is the profit you make minus the cost for the capital you employ is in the wizard industries. It’s where R&D happens; they’re two times more R&D intensive. They’re big stars, the nebulae, where new business is born.- IPMAT - 2025
- Reading Comprehension