Shortcut Tricks of Partnership
1. Two numbers are in the ratio a : b. If p is added to the first number and q is added to the second number respectively, then ratio of the resulting numbers become m : n. Then
the original first number
= [ a (mq - np) ] / (an - bm)
the original second number
=[ b (mq - np)] / (an - bm)
Q. In the class, the number of boys and girls is in the ratio of 4 : 5. If 10 more boys join the category, the ratio of numbers of boys and girls becomes 6 : 5. How many girls are there in the class?
a) 20 b) 30
c) 25 d) Couldn't be determined
Solution : c)
Number of girls = [b (mq - np)] / (an - bm)
= [5 ( 6 ×0 - 5× 10)]/ ( 4×5 - 5×6)
= 25
2. If on adding x to four numbers a, b, c, d; the resulting numbers become proportional then
x = (bc - ad) / [(a + d) - (b + c)]
Q. What must be deducted from each of the numbers 7,10,12 and 18 so that the resultant numbers are in proportion?
a) 1 b) 2
c) 3 d) 4
Solution : b)
Required number = (bc - ad) / [ (a + d) - ((b + c)]
= ( 10×12 - 7 ×18) / [( 7 + 18) - ( 10 + 12)]
= - 6/3
= - 2
Thus 2 must be subtracted from each of the numbers.
3. The ratio between two numbers is a : b, if each number is increased by x, the ratio becomes c : d.
Then sum of two numbers
= [x (a + b) (c - d)] /(ad - bc)
Q. Two numbers are within the ratio 2 : 3. If 4 be added to both of them, then their ratio becomes 3 : 4. Find the sum of the numbers
a) 10 b) 15
c) 20 d) 25
Solution : b)
Sum of two numbers = [ 4 (a +b) (c - d)] /(ad - bc)
= [ 4 (2 + 3) ( 3 - 4)] / (2×4 - 3×3)
= 20
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