19. boats & streams
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This document provides important facts and formulas for boats and streams, along with sample problems and solutions. It states that the direction of a stream is called downstream, while against the stream is upstream. The speed of a boat downstream equals the boat speed plus the stream speed, while upstream it is the boat speed minus the stream speed. Sample problems are given to calculate boat speed in still water and stream rate based on upstream and downstream times.
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IT IS AN IMPORTANT TOPIC FOR ALL COMPETITIVE LEVEL EXAMINATIONS OR GOVT EXAMINATIONS. IT IS VERY HELPFUL FOR THOSE WHO ARE APPEARING FOR THOSE JOB EXAMINATIONS,
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The document discusses concepts related to boats moving with and against streams. It defines that the speed of a boat or swimmer in still water is their baseline speed, and the speed upstream or downstream is calculated by adding or subtracting the stream speed. Several examples are provided to demonstrate calculating distances and stream speeds given time taken to travel upstream and downstream. Formulas are provided to calculate distances and stream/boat speeds using variables for boat speed, stream speed, and time taken to travel distances with or against the current.
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The document discusses concepts related to boats moving with and against streams. It defines that the speed of a boat or swimmer in still water is their baseline speed, and the speed upstream or downstream is calculated by adding or subtracting the stream speed. Several examples are provided to demonstrate calculating distances and stream speeds given time taken to travel upstream and downstream. Formulas are provided to calculate distances and stream/boat speeds using variables for boat speed, stream speed, and time taken to travel distances with or against the current.
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1) The document provides formulas and examples to calculate boat speeds upstream and downstream based on the boat's speed in still water and the speed of the river current.
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3) Several word problems are worked out using the formulas to find values like boat speed in still water and river current speed given upstream and downstream times or distances.
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28. clocks
This document provides information about clocks and time. It includes:
1) Important facts about clock faces being divided into 60 minute spaces and clocks having an hour and minute hand.
2) Examples of calculating time differences between clocks and determining when clock hands will be in certain positions.
3) Explanations and solutions to examples such as finding the angle between hands at a certain time or when hands will be together or perpendicular.
27. calender
This document provides formulas and examples for calculating the day of the week for any given date by determining the number of odd days. It explains that an ordinary year has 1 odd day while a leap year has 2 odd days. To calculate the odd days for a period, you add the odd days for each year in that period. Several examples are given to demonstrate how to use this method to find the day of the week for different dates. The key points covered are that any date in March will fall on the same day of the week as the corresponding date in November of that year, and the calendar can be reused every 4 years.
25. volume & surface area
eO
The document provides 27 examples solving problems related to calculating volumes and surface areas of various geometric shapes like cubes, cuboids, cylinders, cones, spheres, and hemispheres. The key formulas used include formulas for volume and surface area of cubes, cuboids, cylinders, cones, spheres, and hemispheres. Sample problems include finding volumes and surface areas given dimensions, number of cubes or balls that can be made from a given volume, and percentage increases in volumes and surface areas when dimensions change.
24. area
1. The document provides formulas and concepts related to geometry including triangles, quadrilaterals, circles, and other shapes.
2. It includes formulas for calculating the areas of various shapes such as rectangles, triangles, parallelograms, trapezoids, circles, and composite figures.
3. Several solved examples applying these formulas are given at the end to demonstrate calculations of lengths, widths, areas, and perimeters of different geometric shapes.
23. logarithms
This document provides important facts and formulas about logarithms. It defines logarithms and gives examples of evaluating logarithms using properties like loga(xy)=loga(x)+loga(y). It also defines common logarithms as logarithms to base 10, and discusses the characteristic and mantissa of logarithms. Several solved examples are given to illustrate evaluating logarithms and using their properties to simplify logarithmic expressions.
22. compound interest
Compound interest is calculated by adding interest to the principal amount in regular intervals called compounding periods. The principal and previously accumulated interest becomes the basis for calculating interest in the next period. Three key formulas are provided for calculating compound interest compounded annually, semi-annually, and quarterly. Several example problems are then solved demonstrating the application of these formulas to calculate compound interest amounts over different time periods and interest rates.
18. problem on trains
1. The document provides 10 examples of problems involving trains passing each other or passing stationary objects while moving at various speeds. It gives the calculations to determine time taken, speed, length of trains/objects from the information provided in each example.
2. Key formulas provided include converting between km/hr and m/sec, calculating relative speed of trains moving in the same or opposite directions, and determining time taken for trains to pass based on their lengths, speeds and direction of motion.
3. The examples use these formulas to solve for values like time taken, speed, length from the data like one value being given in each problem.
17. time & distance
1. This document provides important formulas and examples related to time and distance problems. It includes formulas for speed, distance, and time as well as examples of speed, average speed, and time calculations for distances covered at different speeds.
2. Several solved examples demonstrate using the formulas and concepts to calculate speeds, times, distances, and average speeds for scenarios like traveling different distances at different speeds, catching up to another traveler, and missing a train by certain times depending on walking speed.
3. The document serves as a reference for the key formulas and concepts needed to solve time and distance word problems.
12. ratio & prapotion
1. Ratio and proportion are important concepts involving relationships between quantities. A ratio represents the fraction between two quantities, while a proportion exists when ratios are equal.
2. Key formulas and concepts include: the product of means equals the product of extremes; finding fourth, third, and mean proportionals; comparing and compounding ratios; and direct and inverse variation.
3. Examples demonstrate calculating ratios, proportions, and proportionals from word problems involving money, mixtures, and other real-world scenarios.
11. profit & loss
The document provides information on profit and loss concepts. It defines key terms like cost price, selling price, profit, gain and loss. It provides formulas to calculate gain, loss, gain/loss percentage. It also includes solved examples like calculating profit/loss percentage when an item is bought and sold at different prices, finding cost price or selling price when other details are given.
10. percentage
eO
This document provides information on percentage including concepts, formulas, and examples. Some key points:
- Percentage means hundredths, so 20% means 20/100 or 1/5.
- To increase or decrease a number by a certain percentage, the percentage is calculated as a fraction of the original number.
- Population and depreciation problems can be solved using the formula: Current value = Original value × (1 ± Rate of change/100)^Number of years.
- Examples provide calculations for percentage of a number, percentage increase/decrease, and multi-step percentage word problems.
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19. boats & streams
- 1. Free GK Alerts- JOIN OnlineGK to 9870807070 19.BOATS AND STREAMS IMPORTANT FACTS AND FORMULA eG K 1.In water ,the direction along the stream is called downstream and ,the direction against the stream is called upstream. 2.If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr,then: speed downstream=(u+v)km/hr. speed upstream=(u-v)km/hr. in 3.If the speed downstream is a km/hr and the speed upstream is b km/hr,then : speed in still water=1/2(a+b)km/hr rate of stream=1/2(a-b)km/hr SOLVED EXAMPLES EX.1.A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current. nl Sol. Rate in still water=1/2(10+7)km/hr=8.5 km/hr. Rate of current=1/2(10-7)km/hr=1.5 km/hr. eO EX.2. A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover a distance of 5km upstream. find the speed of the river current in km/hr. Sol. rate downstream=(15/3 ¾)km/hr=(15*4/15)km/hr=4km/hr. Rate upstream=(5/2 ½)km/hr=(5*2/5)km/hr=2km/hr. Speed of current=1/2(4-2)km/hr=1km/hr Th EX.3. a man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream. Sol. Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph. So,2x=18 or x=9. Rate upstream=9 km/hr,rate downstream=27 km/hr. Hence,rate of stream=1/2(27-9)km/hr=9 km/hr. EX.4. there is a road beside a river.two friends started from a place A,moved to a temple situated at another place B and then returned to A again.one of them moves on a cycle at a speed of 12 km/hr,while the other sails on a boat at a speed of 10
- 2. eG K km/hr.if the river flows at the speed of 4 km/hr,which of the two friends will return to placeA first? Sol. Clearly the cyclist moves both ways at a speed of 12 km/hr. The boat sailor moves downstream @ (10+4)i.e.,14 km/hr and upstream @ (10-4)i.e., 6km/hr. So,average speed of the boat sailor=(2*14*6/14+6)km/hr =42/5 km/hr=8.4 km/hr. since the average speed of the cyclist is greater ,he will return ta A first. EX.5. A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place? in Sol. Speed downstream =(7.5+1.5)km/hr=9 km/hr; Speed upstream=(7.5-1.5)kmph=6kmph. Let the required distance be x km.then, x/9+x/6=50/60. 2x+3x=(5/6*18) 5x=15 x=3. Hence,the required distance is 3km. nl EX.6. In a stream running at 2kmph,a motar boat goes 6km upstream and back again to the starting point in 33 minutes.find the speed of the motarboat in still water. eO Sol.let the speed of the motarboat in still water be x kmph.then, 6/x+2 +6/x-2=33/60 11x2-240x-44=0 11x2-242x+2x-44=0 (x-22)(11x+2)=0 x=22. EX.7.A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours.find the speed of the man in still water and the speed of the current. Th Sol.let rate upstream=x km/hr and rate downstream=y km/hr. Then,40/x +55/y =13…(i) and 30/x +44/y =10 Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11. Substituting y=11 in (i),we get:x=5. Rate in still water =1/2(11+5)kmph=8kmph. Rate of current=1/2(11-5)kmph=3kmph