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Magisetty Harikrushna
Magisetty Harikrushna

The document discusses various concepts related to ratios and proportions involving numbers, mixtures, quantities, prices, and percentages. Some key points covered include: - How to calculate component quantities in a mixture given the total quantity and their ratio. - How to determine original component quantities if something is added or subtracted from the mixture. - How to calculate new ratios that result from adding or subtracting from numbers in a given ratio. - How to determine component percentages in a mixture from the given component ratio. - How to calculate the cost price of a mixture based on component quantities, prices, and desired cost price.

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Note: i). If two numbers are in the ratio of a : b and the sum of these vi). If the ratio of two numbers is a : b, then the number that should be ax bx subtracted from each of the numbers in order to make this ratio c : d is numbers is x, then these numbers will be and Or a b a b bc  ad . If in a mixture of x liters, two liquids A and B are in the ratio of a : b, cd then the quantities if liquids A and B in the mixture will be vii). There are four numbers a, b, c and d. ax bx a). The number that should be subtracted from each of these numbers liters and liters, respectively. a b a b ad  bc so that the remaining numbers may be proportional is . ii). If three numbers are in the ratio of a : b : c and the sum of these (a  d)  (b  c) ax bx cx b). The number that should be added to each of these numbers so that numbers is x, then these numbers will be and . a bc a bc a bc bc  ad the remaining numbers may be proportional is . ii). If two numbers are in the ratio of a : b and the difference of these (a  d)  (b  c) numbers is x, then these numbers will be viii). The income of two persons are in the ratio of a : b and their ax bx ax bx expenditures are in the ratio of c : d. If the saving of each person be Rs. and if a  b, and if a  b a b a b ba ba aS(d  c) bS(d  c) S, then their incomes are given by Rs. and Rs. and iii). The ratio between two numbers is a : b. If x is added to each of ad  bc ad  bc these numbers, the ratio becomes c : d. The two numbers are given as cS(b  a) dS(b  a) their expenditures are given by Rs. and Rs. . ax(c  d) bx(c  d) ad  bc ad  bc and ad  bc ad  bc ix). If in a mixture of x liters of two liquids A and B, the ratio of liquids iv). The ratio between two numbers is a : b. If x is subtracted from each A and B is a : b, then the quantity of liquid B to be added in order to of these numbers, the ratio becomes c : d. The two numbers are given as x(ad  bc) make this ratio c : d is . ax(d  c) bx(d  c) c(a  b) and ad  bc ad  bc x). If in a mixture of x liters of two liquids A and B, the ratio of liquids v). If the ratio of two numbers is a : b, then the number that should be A and B is a : b, then the quantity of liquid A to be added in order to added to each of the numbers in order to make this ratio c : d is x(bc  ad) make this ratio c : d is . ad  bc d(a  b) . cd
xi). If in a mixture of x liters of two liquids A and B, the ratio of liquids A and B is a : b. If on adding x liters of liquid B to the mixture, the ratio of A to B becomes a : c, then in the beginning the quantity of liquid A in ax bx the mixture was liters and that of liquid B was liters. c b c b xii). When two ingredients A and B of quantities q1 and q2 and cost price/ unit c1 and c2 are mixed to get a mixture having cost price/unit cm , then q1 c2  cm c1 q1  c2 q2  and cm  . q2 cm  c1 q1  q2 xiii). If a mixture contains two ingredients A and B in the ratio a : b, a then percentage of A in the mixture is 100% and percentage of B a b b in the mixture is 100% . a b xiv). If two mixtures M1 and M2 contain ingredients A and B in the ratio a : b and c : d respectively, then a third mixture M3 obtained by mixing M1 and M2  ax cy     in the ratio x : y will contain  a  b c  d  100% ingredient A and  xy       bx dy      a  b c  d  100% ingredient B.  xy     

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  • 1. Note: i). If two numbers are in the ratio of a : b and the sum of these vi). If the ratio of two numbers is a : b, then the number that should be ax bx subtracted from each of the numbers in order to make this ratio c : d is numbers is x, then these numbers will be and Or a b a b bc  ad . If in a mixture of x liters, two liquids A and B are in the ratio of a : b, cd then the quantities if liquids A and B in the mixture will be vii). There are four numbers a, b, c and d. ax bx a). The number that should be subtracted from each of these numbers liters and liters, respectively. a b a b ad  bc so that the remaining numbers may be proportional is . ii). If three numbers are in the ratio of a : b : c and the sum of these (a  d)  (b  c) ax bx cx b). The number that should be added to each of these numbers so that numbers is x, then these numbers will be and . a bc a bc a bc bc  ad the remaining numbers may be proportional is . ii). If two numbers are in the ratio of a : b and the difference of these (a  d)  (b  c) numbers is x, then these numbers will be viii). The income of two persons are in the ratio of a : b and their ax bx ax bx expenditures are in the ratio of c : d. If the saving of each person be Rs. and if a  b, and if a  b a b a b ba ba aS(d  c) bS(d  c) S, then their incomes are given by Rs. and Rs. and iii). The ratio between two numbers is a : b. If x is added to each of ad  bc ad  bc these numbers, the ratio becomes c : d. The two numbers are given as cS(b  a) dS(b  a) their expenditures are given by Rs. and Rs. . ax(c  d) bx(c  d) ad  bc ad  bc and ad  bc ad  bc ix). If in a mixture of x liters of two liquids A and B, the ratio of liquids iv). The ratio between two numbers is a : b. If x is subtracted from each A and B is a : b, then the quantity of liquid B to be added in order to of these numbers, the ratio becomes c : d. The two numbers are given as x(ad  bc) make this ratio c : d is . ax(d  c) bx(d  c) c(a  b) and ad  bc ad  bc x). If in a mixture of x liters of two liquids A and B, the ratio of liquids v). If the ratio of two numbers is a : b, then the number that should be A and B is a : b, then the quantity of liquid A to be added in order to added to each of the numbers in order to make this ratio c : d is x(bc  ad) make this ratio c : d is . ad  bc d(a  b) . cd
  • 2. xi). If in a mixture of x liters of two liquids A and B, the ratio of liquids A and B is a : b. If on adding x liters of liquid B to the mixture, the ratio of A to B becomes a : c, then in the beginning the quantity of liquid A in ax bx the mixture was liters and that of liquid B was liters. c b c b xii). When two ingredients A and B of quantities q1 and q2 and cost price/ unit c1 and c2 are mixed to get a mixture having cost price/unit cm , then q1 c2  cm c1 q1  c2 q2  and cm  . q2 cm  c1 q1  q2 xiii). If a mixture contains two ingredients A and B in the ratio a : b, a then percentage of A in the mixture is 100% and percentage of B a b b in the mixture is 100% . a b xiv). If two mixtures M1 and M2 contain ingredients A and B in the ratio a : b and c : d respectively, then a third mixture M3 obtained by mixing M1 and M2  ax cy     in the ratio x : y will contain  a  b c  d  100% ingredient A and  xy       bx dy      a  b c  d  100% ingredient B.  xy     