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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 amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is
Let the amounts Neeta, Geeta, and Sita earn in a day be n, g, and s respectively.
Then, it has been given that:
n+g=6s -i
s+n=2g -ii
ii-i, we get: s-g = 2g-6s
7s = 3g.
Let g be 7a. Then s earns 3a.
Then n earns 6s-g = 18a-7a = 11a.
Thus, the ratio is 11a:3a = 11:3
A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is
Correct Answer: 34
Let price of smallest cup be 2x and medium be 5x and large be y
Now by condition 1
we get $$2x\ \times\ \ 5x\ \times\ y\ =800$$
we get $$x^2y\ =80$$ (1)
Now as per second condition ;
$$\left(2x+6\right)\times\ \left(5x+6\right)\ y\ =3200$$ (2)
Now dividing (2) and (1)
we get $$\frac{\left(\left(2x+6\right)\times\ \left(5x+6\right)\right)}{x^2}=40$$
we get $$10x^2+42x+36\ =\ 40x^2$$
we get $$\ 30x^2-42x-36=0$$
$$5x^2-7x-6=0$$
we get x=2
So 2x=4 and 5x=10
Now substituting in (1) we get y =20
Now therefore sum = 4+10+20 =34
In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
Correct Answer: 43200
In the question, it is given that the ratio of number of literate males to literate females is 2 : 3.
Given, the number of literate males = 3600
The number of literate females = $$\frac{3600}{2}\times3$$ = 5400
Males : Females = 5 : 4
Let the number of males be 5y and the number of females be 4y
Illiterate males = 5y - 3600
Illiterate females = 4y - 5400
It is given,
$$\ \frac{\ 5y-3600}{4y-5400}=\frac{4}{3}$$
15y - 10800 = 16y - 21600
y = 10800
Number of females = 4y = 4*10800 = 43200
Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is
Correct Answer: 111
Let the number of persons standing ahead and behind of Pinky be 3a and 5a.
Total number of persons = 3a + 5a + 1(including pinky) = 8a + 1
8a + 1 < 300
8a < 299
a < 37.375
Maximum value a can take is 37.
The maximum possible number of persons standing ahead of Pinky = 3a = 3*37 = 111
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