IMPORTANT TRICKS:-
Trick(1): Distribute the number A into a:b.
First part = a x A/a+b, 2nd part = b x A/ a+b.
Difference between 1st and 2nd part = difference of a and b /a+b X A = (a - b)/(a+b) X A.
Trick(2): The sum of two numbers is A and their difference a, then the ratio of numbers are A + a : A - a.
Example: The sum of two numbers is 40 and difference is 4, then the ratio of numbers = ?
Soln: Ratio of numbers = 40 + 4 : 40 - 4 = 44 : 36 = 11 : 9.
Trick(3): If the ratio of 1st and 2nd = a : b and 2nd and 3rd = c : d, then the ratio of 1st, 2nd and third is = ac : bc : bd.
Trick(4): The ratio of diagonals of any two squares is a : b then the ratio of their area will be a^2:b^2. Example: The ratio of diagonals of two squares is 2 : 1, then what will be the ratio of their area? Soln: 2^2 : 1^2 = 4 : 1.
Trick(5): If a lit. mixture of milk and water in the ratio of milk and water p : q the quantity of water to be added in order to make the ratio m : n is a(pn - qm) /m(p + q).
Trick(6): A mixture of milk and water in the ratio a : b. If a liters of water to be added the mixture becomes in the ratio a : c. The quantity of milk = an / c-b), water = bn / (c-b).
Trick(7): The income of two persons are in the ratio p:q and their expenditure in the ratio m : n If each of them saves Rs. a, then their income are given by ap(n - m)/(pn - qn) and aq(n - m)/(pn - qn).
Trick(1): Distribute the number A into a:b.
First part = a x A/a+b, 2nd part = b x A/ a+b.
Difference between 1st and 2nd part = difference of a and b /a+b X A = (a - b)/(a+b) X A.
Trick(2): The sum of two numbers is A and their difference a, then the ratio of numbers are A + a : A - a.
Example: The sum of two numbers is 40 and difference is 4, then the ratio of numbers = ?
Soln: Ratio of numbers = 40 + 4 : 40 - 4 = 44 : 36 = 11 : 9.
Trick(3): If the ratio of 1st and 2nd = a : b and 2nd and 3rd = c : d, then the ratio of 1st, 2nd and third is = ac : bc : bd.
Trick(4): The ratio of diagonals of any two squares is a : b then the ratio of their area will be a^2:b^2. Example: The ratio of diagonals of two squares is 2 : 1, then what will be the ratio of their area? Soln: 2^2 : 1^2 = 4 : 1.
Trick(5): If a lit. mixture of milk and water in the ratio of milk and water p : q the quantity of water to be added in order to make the ratio m : n is a(pn - qm) /m(p + q).
Trick(6): A mixture of milk and water in the ratio a : b. If a liters of water to be added the mixture becomes in the ratio a : c. The quantity of milk = an / c-b), water = bn / (c-b).
Trick(7): The income of two persons are in the ratio p:q and their expenditure in the ratio m : n If each of them saves Rs. a, then their income are given by ap(n - m)/(pn - qn) and aq(n - m)/(pn - qn).
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