Percent changes in price and consumption
The total cost to build a table is two-folds – one, the cost of raw material consumed and two, the labour cost. Further, the labour cost is calculated as a percentage of the cost of raw material consumed. Due to changes in the supply and labour situation, the price of raw material increased by 25% and also the labour cost increased from 20% of cost of raw material to 32% of cost of raw material. If the total cost to build a table needs to be the same, find the percentage reduction in consumption of raw material used. 27.2727...% Approach 1: We have already seen, how to find the percentage increase in total cost of the table. Next, consider this as a stand-alone standard question ..... if the percentage increase in price is ...%, by what percentage should consumption reduce to main the expenditure? I am sure, [...]
Percentage changes in raw material and labour
The total cost to build a table is two-folds – one, the cost of raw material consumed and two, the labour cost. Further, the labour cost is calculated as a percentage of the cost of raw material consumed. Due to changes in the supply and labour situation, the price of raw material increased by 25% and also the labour cost increased from 20% of cost of raw material to 32% of cost of raw material. What was the percentage increase in the total cost to build a table? 37.5% Consider the original raw material cost as 100. Now find the original labour cost. Next, find the new raw material cost and the new labour cost, as required % of this new raw material cost. Let original cost of raw material be Rs. 100 Thus, labour cost will be 20% of 100 i.e. Rs. 20 . And original [...]
Self Study or Live Classes?
Few pointers to help you decide whether you should opt for a Self Study Course or a Live Class Course 1. Your learning style “As a college student, I rarely attended classes. I found them to be a huge waste of time. I would prefer to refer to books from the library and study on my own, at my own schedule and pace. Never did I feel that I was missing out on something. And, yes, I was among the toppers in my class” If the above describes you well enough, then Self Study courses is an obvious choice for you. On the other hand, you may be the studious kind, who rarely misses classes in your college and who actually gains from being regular in classes …. again the choice is obvious – Live Class course. 2. Self-driven or motivated by peers and regular interaction In Self Study courses, [...]
Avoiding calculations in a CI question
Question On a certain sum of money, the compound interest earned at the end of three years is Rs. 2,382 and the compound interest at the end of two years is Rs. 1,518. Find the principal. Well there is no suitable hint that can be given, since it is more of a intelligent number-play to guess the multiplying factor corresponding to interest rate, so at best, let us see some examples when interest rates are known. If the interest rate is 10%, the ratio of CI in any two consecutive years will be 10 : 11. And the CI in 1st, 2nd and 3rd year will be in the ratio 100 : 110 : 121. If the interest rate is 12.5%, the ratio of CI in any two consecutive years will be 8 : 9. And the CI in 1st, 2nd and 3rd year will be in the ratio [...]
Maximum that can fail? Wt Avg
Question 38 students took a test that had 100 as the maximum mark and 35 as passing marks. If the average marks of all the 38 students was 78, find the maximum number of students that could have failed? Answer: 12 students Points to ponder 1. It can be thought as distributing a total of 38 × 78 = 2964 amongst 38 students such that the set of students who received less than 35 marks is as high as possible. 2. One simple trivial start will be giving all the students 0 marks. But this way, nothing of the 2964 marks will distributed. And we have to distribute these marks amongst these 38 students ... entirely ... without anything left with us. Since we have a lot of marks on hand, 2964, let us distribute more marks to each student .... but we also need maximum of [...]
Work – men join or leave daily
Question 8 men started a job and worked on it for 12 days. From the 13th day onwards, 1 new worker joined them everyday till the job was finished in a total of 20 days. If the same job has to be done starting with n workers and one worker quits at the end of every day, then what is the minimum value of n? And if you want a more challenging question .....with the same data as above .... if n is the least possible value, then how many days will it take for the work to get done? Step 1: Express the total work in man-days. 8 men for 12 days and then 9, 10, 11, 12 .... men on each of the following day, till the 20th day. Step 2: In second case, we start with n men and each day one man reduces. Thus, [...]
Diamond – weight, value
Question The value of a diamond varies directly as the square of its weight. A diamond falls and breaks into 3 pieces with their weights in the ratio 1 : 2 : 3. Had the three pieces been equal in weight, the loss in value would have been a further Rs. 4,500. Find the value of the original unbroken diamond. Consider the weights in the three cases ... Case 1: Weight of the three pieces as they broke Case 2: Weight of the unbroken diamond (there is no loss of weight when diamond breaks) Case 3: Weight of the three pieces, had they been equal. Next square the weights and work in value in the three cases. First working on the weights in three cases ... Case 1: The pieces as they broke .... let weights be k, 2k and 3k Case 2: The unbroken diamond ... the [...]
Free Study Material for CAT Prep
Students usually understand Study Material to mean printed books that explain the concepts, have solved examples and practice exercises. True, printed material was the norm till videos took over. It is far easier to explain concepts through a video than through text. Also exams are now mostly online and students need to practice solving questions online. With these changes, our printed study material ... we call them Fundabooks ... got redundant. But there are some advantages of printed material ... it is more active participation, is easier to revise. So we are providing the PDFs of the Fundabooks here, for free. The explanation of theory/concepts in the books is super. There are exercises for you to check your understanding. However we have removed the practice question bank, which are available in our paid online courses. Number Systems Fundabook Arithmetic Algebra Geometry P & C, Probability Miscellaneous Quant Data Interpretation Logical [...]
Distribute 5 pieces of Pizza amongst 3 friends
To be good with unusual or seemingly complex questions, you need to be good with basic rules of counting i.e. breaking the question, based on the conditions given, into easier manageable cases; sometimes work on piece-meal basis i.e. assign an object to a position and proceed like-wise, object by object i.e. dont expect some great unifying theory or approach that solves the entire question in one go. Basically more complex a question seems, let go of standard monolithic approaches and fallback on rudimentary counting techniques. A example of this type .... A circular pizza is cut into 5 sectors, each of a different size. The sectors are then distributed amongst 3 friends such that each friend receives atleast one sector and no friend receives any adjacent sectors. In how many ways can the pizza pieces be distributed amongst the 3 friends? Task 1: How many ways can the [...]
Popular PYQ of CAT – Escalator
Excellent problem to learn putting ratios to their optimum use. Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? 1. 40 2. 50 3. 60 4. 80 Now for the ‘wow’ solution … Since the ratio of speeds of Shyam and Vyom is 3 : 2 and the distance that each travels is 25 : 20, the ratio of the time in which they reach the top is (25/3) : (20/2) i.e. 5 : 6. Thus, if [...]