TLDR;
Alright guys, so this session is all about mastering the ratio method for upcoming bank exams. We're going to see how to use it across different arithmetic topics, from basic to advanced level questions. The session highlights the importance of percentage as a "king maker" for ratios and focuses on techniques to save time on questions, which will ultimately help you score better.
- Ratio method is key for arithmetic.
- Successive and balancing are important concepts.
- Smart work is essential to score better.
Introduction to Ratio Method [0:14]
So, welcome everyone to the session. Today, we're diving deep into how to use the ratio method in upcoming bank exams. We'll be covering everything from the basics to the advanced stuff, so you can ace those arithmetic problems. If you're just joining, a big welcome to you. Make sure you like and share the session so more people can benefit from these concepts. And after the session, do leave your valuable feedback so we know what you learned.
Importance of Percentage and Ratio [1:17]
When it comes to arithmetic, ratio is often called the king. But remember, percentage is the king maker. You can't really use ratios without a good understanding of percentages. If you know your percentages and ratios, I'll take care of the rest and show you how to tackle even the toughest questions.
Course Information [3:17]
If you want a complete and detailed preparation for quantitative aptitude for bank or insurance exams, check out our "Sampoorna" batch. It's a one-stop solution with both foundation and practice access. In the foundation, we're currently covering Time and Work, and we'll soon move on to other topics like Time, Speed, Distance, Permutation, Combination, Probability, Mensuration and DI. In practice, we've already completed topics like Percentage, Ratio, Average, Mixture Allegation, and Partnership. Next up is Ages. If you only want practice, you can opt for the "Sadhna" batch, which is a part of "Sampoorna" but more affordable.
Ratio Method: Basic vs Advanced [5:02]
In previous sessions, we tackled shorter questions, focusing on prelims level exams. But today, we're taking it to the next level. We'll see how to apply ratios in unpredictable scenarios and more complex questions. To effectively use the ratio method, you need to understand successive and balancing. Successive is the "baap" of everything, and balancing is important for every topic.
Understanding Successive [6:01]
Let's quickly understand successive. Suppose you increase something by 20%, then decrease it by 50%, and then increase it by 30%. How do you find the effective change? If you increase by 20%, it goes from 5 to 6. Decreasing by 50% means it goes from 2 to 1. Increasing by 30% means it goes from 10 to 13. Overall, your item goes from 100 to 78.
Application of Successive [8:50]
Let's see where you can use this. Imagine an article with a cost price of ₹12,000. You mark it up by 20%, give a discount of 50%, and then apply a tax of 30%. What will the customer pay? Instead of doing it step by step, use the ratio method. A 20% increase means 6/5, a 50% decrease means 1/2, and a 30% increase means 13/10. So, the article goes from 100 to 78. If 100 is ₹12,000, then 78 is ₹9360.
Question 1: Amount Spent [10:46]
A person has some amount. 24% is stolen, which is 6/25. So, 25 becomes 19. Then 45% is lost, which is 9/20. So, 20 becomes 11. Then 36.36% is spent on food, which is 4/11. So, 11 becomes 7. Finally, he purchases a book for ₹266. What was the initial amount? Multiply the ratios: 25 * 20 = 500 and 19 * 7 = 133. If 133 is ₹266, then 500 is ₹1000.
Question 2: Salary Based [13:34]
A spends 24% on rent, which is 6/25. So, 25 becomes 19. Then 20% of the remaining on food, which is 1/5. So, 5 becomes 4. Then 50% of the remaining on travelling, which is 1/2. So, 2 becomes 1. The difference between the amount spent on travelling and food is ₹5700. What is the income? Balance the ratios. If 5 becomes 4, then 4 becomes 2. The difference between food and transport is 1, which is ₹5700. So, 5 is 5700 * 5. If 19 parts is 5700 * 5, then 25 parts is (5700 * 5 * 25) / 19 = ₹37,500.
Question 3: Price of Rice [18:26]
When the price of rice increases by 40%, which is 2/5, so 5 becomes 7. A housewife wants to increase her expenditure by only 12%, which is 3/25, so 25 becomes 28. By what percent should she reduce the quantity? Price and quantity multiply to give expenditure. So, 5 * 5 = 25 and 7 * 4 = 28. The quantity goes from 5 to 4. So, the reduction is 1/5, which is 20%.
Question 4: Expenditure [20:41]
I spent 20% on food, then 30% of the remaining on transport, then 16.66% on medicines, and 8.33% on travelling. What is the total expenditure? 20% means 5 becomes 4. 30% means 10 becomes 7. 16.66% means 6 becomes 5. 8.33% means 12 becomes 11. So, the money goes from 180 to 77. The expenditure is 103 parts.
Profit and Loss: Same Cost Price [24:02]
If two articles are bought at the same cost price, one is sold at a 30% profit and the other at a 30% loss, what is the overall profit or loss? If the cost price is 100 for both, then the selling prices are 130 and 70. The total cost price is 200 and the total selling price is 200. So, there is no profit or loss.
Question 5: Profit and Loss [28:37]
A person sold two articles at the same price. On the first, he makes a 12% profit, which is 3/25. So, 25 becomes 28. The difference between the profits is ₹150. The overall profit is 40%, which is 2/5. So, 5 becomes 7. If the selling price is 28 for both, then the total selling price is 56. So, the total cost price is 40. If the first cost price is 25, then the second is 15. The difference in profit is 10, which is ₹150. So, one part is 15. The cost price of the first article is 25 * 15 = ₹375.
Sound Issue Fix [31:45]
Fixing sound issue and repeating the solution.
Question 5: Profit and Loss (Repeated) [32:13]
Repeating the solution.
Question 6: Shopkeeper Sold an Article [34:00]
A shopkeeper sold an article at a 40% loss, which is 2/5. So, 5 becomes 3. If he had bought it for ₹150 more and sold it for ₹190 more, the loss would have been only 20%, which is 1/5. So, 5 becomes 4. What is the initial cost price? Use cross product. 5 * 4 = 20 and 5 * 3 = 15. The difference is 5. 150 * 4 = 600 and 190 * 5 = 950. The difference is 350. If 5 parts is 350, then 5 parts is 350.
Question 7: Shopkeeper Marked Up [38:08]
A shopkeeper marked up an article 60% above the cost price, which is 3/5. So, 5 becomes 8. He gave a discount of 25%. So, 8 becomes 6. The profit is ₹475. The profit is 1 part, which is ₹475. The cost price of article B is 40% more than A. So, if A is 5, then B is 7. The profit on both is the same. So, the selling price of B is 7 + 1 = 8. 8 * 475 = ₹3800.
Question 8: Simple and Compound Interest [40:12]
₹x + 200 is invested in scheme A at r% simple interest, and ₹x - 300 is invested in scheme B at 2r% simple interest. After 4 years, the interest from A is 25% less than B. What is the value of x? The ratio of returns is 1:2. The ratio of interest is 3:4. So, the ratio of investments is 3:2. If x + 200 / x - 300 = 3/2, then x = 1300.
Compound Interest Concept [44:33]
Compound interest is based on ratios. If the rate is 16.66%, which is 1/6, then the money increases from 6 to 7 every year.
Question 9: Compound Interest [44:51]
If ₹56,000 yields a compound interest of ₹8827 in 9 months, compounded quarterly, what is the rate per annum? The interest is calculated three times. So, the money goes from 56000 to 64827. This simplifies to 8000 to 9261, which is 20^3 to 21^3. So, the rate per quarter is 5%. The annual rate is 20%.
Question 10: Compound Interest Time [50:38]
At what time will ₹15360 yield a compound interest of ₹6510 at 12.5% per annum? 12.5% is 1/8. So, the money increases from 8 to 9. The money goes from 15360 to 21870. This simplifies to 512 to 729, which is 8^3 to 9^3. So, the time is 3 years.
Question 11: Mixed Interest [53:34]
₹2x and ₹x are invested at 5% simple interest and 8% compound interest, respectively. The difference in interest is ₹840. What is the value of x? The compound interest increases from 625 to 729, which is 104 parts. The simple interest is 125 parts. The difference is 21 parts, which is ₹840. So, one part is 40. The value of x is 625 * 40 = ₹25,000.
Question 12: Mixture [56:21]
In a mixture, milk is 6 liters more than water. 40 liters of a second mixture is added, where water and milk are in the ratio 3:5. The new ratio of water to milk is 9:13. What is the final quantity of water? If water is x, then milk is x + 6. The second mixture has 15 liters of water and 25 liters of milk. So, the new ratio is (x + 15) / (x + 31) = 9/13. The difference is 4 parts, which is 16. So, one part is 4. The total quantity of water is 9 * 4 = 36.
Question 13: Vessel with Milk and Water [1:00:44]
A vessel has milk and water in the ratio 5:2. 22 liters of the mixture are removed, and 32 liters of water are added. The new ratio is 7:6. What is the initial quantity of the mixture? The ratio of milk to water is 5:2. After removing 22 liters and adding 32 liters of water, the ratio becomes 7:6. Make the milk equal. So, 35:14 and 35:30. 16 parts is 32. So, one part is 2. The total quantity after removing 22 liters is 49 * 2 = 98. The initial quantity is 98 + 22 = 120.
Question 14: Mixture with Alcohol and Water [1:04:01]
A Z liter mixture contains alcohol and water in the ratio 5:3. x liters of the mixture are taken out. The quantity of alcohol in the resultant mixture is equal to the initial quantity of water. What is the value of x/2 if 54 liters of water remain? If water is 54, then alcohol is 90. So, the initial water was 90. The total mixture was 240. The remaining mixture is 144. So, x is 96. x/2 is 48.
Question 15: Mixture with Milk and Water [1:06:23]
A mixture of 85 - y liters contains milk and water. The quantity of water is x liters less than the total mixture. If y + 32 liters of water are added, the ratio of milk to water becomes 5:4. What is the value of x? The total is 85 - y. Adding y + 32 gives 117. The ratio is 5:4. So, milk is 65 and water is 52. Milk is x. So, x is 65.
Question 16: Vessel Full of Milk [1:09:38]
A vessel is full of milk. A person draws 25% of the quantity and replaces it with water. This process is repeated three more times. 810 ml of milk remains. What was the starting amount of milk? The milk decreases by 25% each time. So, 4 becomes 3. After three times, 64 becomes 27. If 27 is 810, then 64 is 1920.
Question 17: Vessel with Pure Milk [1:14:35]
A vessel contains 54 liters of pure milk. A certain amount is drawn off and the same amount of water is added. The same quantity of mixture is removed and the same quantity of water is added. Now the mixture contains 30 liters of water. What is the drawn-off quantity? The initial milk is 54. The final milk is 24. The ratio is 9:4. So, each time the ratio is 3:2. The amount removed is 1/3 of 54, which is 18.
Question 18: Z Liters of Pure Milk [1:18:14]
There was z liters of pure milk in a container. n/7 of the milk was replaced with water. Again, 2/9 of the mixture is extracted and an equal amount of water is added. If the ratio of water and milk in the final mixture becomes 5:4, what is the value of n? The milk goes from 7 to 7-n. Then it goes from 9 to 7. The final ratio is 5:4. So, the total is 9. The final milk is 4. So, 7-n = 4. n = 3.
Ages: Difference Between Two Persons [1:26:19]
The age difference between two persons always remains the same.
Question 19: Ages [1:27:15]
19 years ago, the ratio of ages of A and B was 9:5. 15 years later, the ratio will be 11:8. What is the present age of A? The difference in the ratio should be the same. The difference is 4 and 3. Make it the same by multiplying by 3 and 4. So, 27:15 and 44:32. The difference is 17 parts, which is 34 years. So, one part is 2. The age 19 years ago was 27 * 2 = 54. The present age is 54 + 19 = 73.
Question 20: Ages Cross Product [1:30:24]
The ratio of the present ages of A and B is 7:9. The ratio of A's age 6 years ago and B's age 8 years later is 5:6. What is the ratio of A's age 4 years hence and B's age 8 years ago? Use cross product. 7 * 6 = 42 and 9 * 5 = 45. The difference is 3. 5 * 8 = 40 and 6 * 6 = 36. The sum is 76. 3 parts is 76. One part is 76/3. The present ages are 7 * 76/3 and 9 * 76/3. A's age 4 years hence is 7 * 76/3 + 4 and B's age 8 years ago is 9 * 76/3 - 8.
Partnership: A Started a Business [1:32:44]
A started a business with ₹1200. After x months, B joined with ₹3600. After 2 more months, C joined with ₹y. The annual profit share is equal. What is the value of y? The investment of A is 1200 * 12. The investment of B is 3600 * (12 - x). The investment of C is y * (10 - x). The ratio of capital is 1:3. So, the ratio of time is 3:1. If 3 parts is 12, then 1 part is 4. So, 12 - x = 4. x = 8. The time for C is 10 - 8 = 2. The investment of C is 14400 / 2 = 7200.
Question 21: Partnership [1:36:13]
P and Q started a business by investing ₹15,000 and ₹15,000 + x. After 4 months, Q withdrew 40% of his initial investment. After a year, the total profit was ₹47,000, and the profit share of Q was ₹22,000. What is the value of 2x? Let the investments be 5A and 5B. After 4 months, Q withdrew 40%. So, 5A * 12 and 5B * 4 + 3B * 8. The ratio is 15A and 11B. The ratio of profits is 25:22. So, 15A/11B = 25/22. A/B = 5/6. If 5A is 15000, then A is 3000. B is 3600. 5B is 18000. x is 3000. 2x is 6000.
Question 22: Partnership Coincidence [1:41:50]
A, B, and C started a business with initial investments of x + 4000, 4500, and 7000. After 1 year, A, B, and C invested an additional 2000, x + 500, and x + 4500, respectively. Find the profit share of B at the end of 2 years if the total profit is 6600. The investments are 2x + 10000, x + 9500, and x + 18500. The profit share of B is (x + 9500) / (4x + 38000) * 6600. If x + 9500 is 1/4 of 4x + 38000, then the profit share is 1/4 * 6600 = 1650.
Question 23: Partnership Active Partner [1:45:29]
M and N started a business with ₹18,000 and ₹x for 10 months and 1 year, respectively. 40% of the total profit is given to M for being an active partner. The remaining profit is divided according to their investments. The profit ratio of M and N is 5:3. What is the value of x? The ratio of capital is 1:3. So, the ratio of time is 3:1. If 3 parts is 12, then 1 part is 4. The time for N is 4. The profit ratio is 5:3. If 40% is for M, then 60% is divided. So, 3.2 and 1.8. The ratio is 3:5. So, 18000/x = 3/5. x = 30000.
Question 24: Time and Work [1:50:30]
A and B together can complete a work in T days. A and B alone take 6x and 5x days, respectively. A alone worked for 11 days, and then B joined. Together they completed the remaining work in 31 days. What is T? The ratio of time is 6:5. So, the ratio of efficiency is 5:6. A worked for 11 days, so 5 * 11. Then A and B worked for 31 days, so (5 + 6) * 31. The total work is 5 * 11 + 11 * 31 = 11 * 36. The time taken by A and B together is 11 * 36 / 11 = 36.
Question 25: Time and Work [1:53:19]
A, B, and C can complete a piece of work in 16, 24, and 12 days, respectively. Together they can complete the work in 5 1/3 days less than A and B together. In how many days can A, B, and C together complete the work? The ratio of time is 4:6:3. The ratio of efficiency is 3:2:4. The efficiency of A, B, and C is 9. The efficiency of A and B is 5. The time ratio is 5:9. The difference is 4, which is 16/3. So, one part is 4/3. The time for A, B, and C is 5 * 4/3 = 20/3.
Question 26: Time Speed and Distance [1:58:18]
A takes twice the time to cover a distance d km than B to cover 2d km. A started from his home, and after 30 minutes, B started from the same house and overtook A after travelling 20/3 km. What is the speed of B? The ratio of distance is 1:2. The ratio of time is 2:1. So, the ratio of speed is 1:4. The ratio of time is 4:1. The difference is 3 parts, which is 30 minutes. So, one part is 10 minutes. B took 10 minutes to travel 20/3 km. So, the speed is 20/3 / (10/60) = 40 km/h.
Question 27: Train [2:04:19]
The length of train A is 400 meters, and the length of train B is x meters more than A. The speeds of both trains are equal. They cross a pole in 16 seconds and 24 seconds. In what time will train B cross a 2x meter long platform? The ratio of time is 2:3. So, the ratio of length is 2:3. If the length of A is 400, then the length of B is 600. x is 200. 2x is 400. The time to cross the platform is 24 + 16 = 40 seconds.
Question 28: Efficiency [2:08:19]
A is 40% less efficient than B, who can do the same work in 20% less time than C. If A and B together complete 80% of the work in 12 days, in how many days can 60% of the work be completed by B and C? The ratio of efficiency of A and B is 3:5. The ratio of time of B and C is 4:5. So, the ratio of efficiency is 5:4. A and B together can do 8 units of work. 8 * 12 is 80% of the work. So, the total work is 8 * 12 * 5/4. 60% of the work is 8 * 12 * 5/4 * 3/5. B and C together can do 9 units of work. So, the time is 8 * 12 * 5/4 * 3/5 / 9 = 8.
Question 29: Train Length [2:11:15]
The length of train A is x meters, and the length of train B is y meters. Train A and train B cross a pole in 8 seconds and 26 seconds. Find the time taken by train A to cross train B when both trains are running in opposite directions with the speed ratio of A to B as 5:4. The length of A is 5 * 8 = 40. The length of B is 4 * 26 = 104. The total length is 144. The relative speed is 5 + 4 = 9. The time is 144 / 9 = 16.
Question 30: Boat and Stream [2:14:01]
The ratio of the speed of the boat in still water to the speed of the stream is 7:5. The total time taken by the boat to cover d km distance in downstream and return 2/3 of the distance is 15 hours. Find the extra time required to reach the starting point. The ratio of downstream and upstream speed is 12:2, which is 6:1. The ratio of distance is 3:2. The ratio of time is 1:4. The total time is 5 parts, which is 15 hours. So, one part is 3 hours. The time to return is 4 * 3 = 12 hours. The time to travel the remaining 1/3 is 6 hours.
Question 31: Downstream and Upstream Speed [2:19:37]
The downstream and upstream speeds are 2.4a and 1.8a. A boat starts in the downstream direction and after travelling 320 km, it returns to the initial point such that the speed of the stream becomes 3/5 of the actual stream. If the journey is completed in 9 hours, what is the original downstream speed? The ratio of downstream and upstream speed is 4:3. The ratio of boat and stream is 7:1. The stream becomes 3/5. So, the boat is 35 and the stream is 5. The downstream speed is 40 and the upstream speed is 32. The ratio is 5:4. The time ratio is 4:5. The total time is 9 hours. So, one part is 1 hour. The downstream time is 4 hours. The downstream speed is 320 / 4 = 80 km/h.
Question 32: Probability [2:23:05]
A box has 6 blue balls, x red balls, and 10 green balls. The probability of choosing a red ball is 1/3. A bag has 6 blue balls, y red balls, and 10 green balls. The probability of choosing a blue ball is 3/10. Find the sum of x and y. If the probability of red is 1/3, then the total is 3 parts. The red is 1 part. The blue and green are 2 parts, which is 16. So, one part is 8. x is 8. If the probability of blue is 3/10, then the total is 10 parts. The blue is 3 parts, which is 6. So, one part is 2. The total is 20. The red is 20 - 6 - 10 = 4. y is 4. x + y = 8 + 4 = 12.
