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Equivalence of ratios: $$a : b = ak : bk$$, where $$k$$ is a constant.
$$a,b,c,d$$ four terms are in proportion.
Invertendo: $$a:b=c:d$$ then $$b:a=d:c$$
Alternendo: $$a:b=c:d$$ then $$a:c=b:d$$
Componendo: $$a:b=c:d$$ then $$\dfrac{a+b}{b}=\dfrac{c+d}{d}$$
Dividendo: $$a:b=c:d$$ then $$\frac{a-b}{b}=\frac{c-d}{d}$$
Componendo-Dividendo: $$a:b=c:d$$ then $$\dfrac{a+b}{a-b}=\dfrac{c+d}{c-d}$$
The number of students in a school is a prime number less than 500. Which of the following can be a possible ratio of the number of boys to girls?
The total number of students in the school is a multiple of the sum of the ratios of boys and girls.
As the total number of students is a prime, it equals the sum of the ratios of boys and girls.
Among the options given, only 18:13 is valid as 18+13=31 is a prime.
The other sums, 212+217 = 429, 221+252=473 and 18+31=49 are all composite.
Two farms A and B have 10 sheep each in January 2000. At the start of each year, 105 sheep are added to A and the number of sheep in B is doubled. What is the ratio of the number of sheep in A and B in February 2006?
Number of sheep in A =640 and number of sheep in B is 640. So, ratio is 1:1
A maid was promised a salary of Rs. 21,000 per year and six saris at the end of the year. If after 8 months, she receives Rs. 14,000 and four saris, what is the value of each sari?
(21000+6S) = 12/8 *(14000+4S)
This holds true for any value of S
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