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Study Material and Tips

### Tips to Solve Problems on Time and Distance

1. 2. x km/hr = 3. x m/sec = 4. If the ratio of the speeds of A and B is a:b , then the ratio of the times taken by them to cover the same distance is or b : a 5. Suppose a man covers a certain distance at x km/ hr and an equal distance at y km/hr . Then, the average speed during the whole journey iskm/hr....

### Tips to Solve Problems on Time and Work

1. If A can do a piece of work in n days, then A's 1 day's work = 2. If A’s 1 day's work =, then A can finish the work in n days. 3. A is thrice as good a workman as B, then: Ratio of work done by A and B = 3 : 1. Ratio of times taken by A and B to finish a work = 1 : 3. NOTE : Whole work...

### Tips to Solve Problems on Chain Rule

1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent. Ex. 1. Cost is directly proportional to the number of articles. (More Articles, More Cost) Ex. 2. Work done is directly proportional to the number of men working on it (More Men,...

### Tips to Solve Problems on Percentage

I.Concept of Percentage : By a certain percent , we mean that many hundredths. Thus x percent means x hundredths, written as x%. To express x% as a fraction : We have , x% = x/100. Thus, 20% = 20/100 = 1/5; 48% = 48/100 = 12/25, etc. To express a/b as a percent : We have, % . Thus, % = 25%; &am...

### Tips to Solve Problems on Decimal Fractions

I. Decimal Fractions : Fractions in which denominators are powers of 10 are known as decimal fractions. Thus ,1/10 = 1 tenth = .1; 1/100 = 1 hundredth = .01; 99/100 = 99 hundreths = .99; 7/1000 = 7 thousandths = .007,etc II. Conversion of a Decimal Into Vulgar Fraction : Put 1 in the denominator under the decimal point and annex with it as many zeros ...

### Tips to Solve Problems on Numbers

I. Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number. A group of digits, denoting a number is called a numeral. We represent a number, say 689745132 as shown below : We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'. II. Plac...

### Tips to Solve Problems on Ratio and Proportion

1. RATIO: The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a:b. In the ratio a:b, we call a as the first term or antecedent and b, the second term or consequent. Ex. The ratio 5: 9 represents 5/9 with antecedent = 5, consequent = 9. Rule: The multiplication or division of each term of a ratio by the same n...

### Tips to Solve Problems on Partnership

Partnership: When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership. Ratio of Division of Gains: (i) When investments of all the partners are for the same time, the gain or loss is distributed a among the partners in the ratio of their investments. Suppose A and B invest Rs. x and Rs. y ...