Ratio and Proportion 1/4

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25. Three friends divide Rs.624 among themselves in the ratio $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$. The share of the third friend is :
a. Rs.288
b. Rs.192
c. Rs.148
d. Rs.144

Answer: D
Explanation:
Multiplying the entire ratio by 12 we get,
Ratio = $\displaystyle\frac{1}{2}:\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}$ = 6:4:3
Share of third friend = Rs.$\left( {624 \times \displaystyle\frac{3}{{13}}} \right)$
= Rs.144

26. One year ago the ratio between Laxman's and Gopal's salary was 3:4. The ratio's of their individual salaries between last year's and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :
a. Rs.1040
b. Rs.1650
c. Rs.2560
d. Rs.3120

Answer: B
Explanation:
Let the salaries of Laxman and Gopal one yer before be $3x$ and $4x$.
Given that laxman's last year and present year salary are in the ratio $4 : 5$.
So his present salary $ = \dfrac{5}{4} \times 3x $$= \dfrac{{15x}}{4}$
Also Gopal's last year and present year salary are in the ratio $2 : 3$
So his present salary $ = \dfrac{3}{2} \times 4x$ $= 6x$
But given that sum of the salaries = $ = \dfrac{{15x}}{4} + 6x = 4290$
$ \Rightarrow \dfrac{{39x}}{4} = 4290$
$ \Rightarrow \require{cancel}\Rightarrow \cancel{39}x = \cancel{4290}^{110} \times 4$ $=440$
Laxman's present salary $=\dfrac{{15x}}{4}$ $= \dfrac{{15}}{4}\times 440 = 1650$

27. Students in Class I, II and III of a school are in the ratio of $3 : 5 : 8$. Had 15 more students admitted to each class, the ratio would have become 6 : 8 : 11. How many total students were there in the beginning?
a. 112
b. 64
c. 96
d. 80

Answer: D
Explanation:
Increase in ratio for 3 classes is $6 - 3 = 8 - 5 = 11 - 8 = 3$.
Given, 15 more students are admitted to each class.
$ \therefore$$3:15 \equiv 16:x$
$ \Rightarrow x = \dfrac{{15 \times 16}}{3} = 80$
$\therefore $ Total students in the beginning = $80$.

28. A spends 90% of his salary and B spends 85% of his salary. But savings of both are equal. Find the income of B, if sum of their incomes is Rs. 5000.
a. 2000
b. 2400
c. 2125
d. 2400

Answer: A
Explanation:
Let the incomes of A and B are x, y respectively.
Savings of $A = (100 - 90)% (x) = 10% (x)$
Savings of $ B = (100 - 85)% (y) = 15% (y)$
Given, both saves equal amount.
Therefore, $10% (x) = 15% (y)$ $ \Rightarrow \dfrac{x}{y} = \dfrac{{15\% }}{{10\% }} = \dfrac{3}{2}$
Therefore, $x : y = 3 : 2$
Hence, B's salary = $\dfrac{{\rm{2}}}{{(2 + 3)}} \times 5000$ $= Rs. 2000.$

29. $x$ is directly proportional to $y$. When $x = 3$ then $y = 7$. If $x = 9$ then $y = ?$
a. 26
b. 24
c. 21
d. 20

Answer: C
Explanation:
$x \propto y$
$ \Rightarrow \dfrac{{{x_1}}}{{{x_2}}} = \dfrac{{{y_1}}}{{{y_2}}}$
$ \Rightarrow \dfrac{3}{9} = \dfrac{7}{{{y_2}}}$
$ \Rightarrow {y_2} = \dfrac{{9 \times 7}}{3} = 21$

30. A car travels 200km at the speed of 40 kmph in certain time. If the speed of the car increases to 60 kmph then distance travelled by the car is ?(Time is same)
a. 240
b. 300
c. 360
d. 325

Answer: B
Explanation:
$D = S \times T$ $ \Rightarrow D \propto S$ ($\because $ Time is constant)
$ \Rightarrow \dfrac{{{D_1}}}{{{D_2}}} = \dfrac{{{S_1}}}{{{S_2}}}$
$ \Rightarrow \dfrac{{200}}{{{D_2}}} = \dfrac{{40}}{{60}}$
$ \Rightarrow {D_2} = \dfrac{{200 \times 60}}{{40}} = 300$

31. $x$ is inversely proportional to $y$. When $x = 9$ then $y = 7$. If $x = 3$ then $y = ?$
a. 21
b. 7/3
c. 3/7
d. 27/7

Answer: A
Explanation:
$x \propto \dfrac{1}{y}$
$ \Rightarrow xy = k$
$ \Rightarrow {x_1}{y_1} = {x_2}{y_2}$
$ \Rightarrow 9 \times 7 = 3 \times {y_2}$
$ \Rightarrow {y_2} = 21$

32. A car covers certain distance at the speed of 40 kmph in 5 hours. If the speed of the car increases to 50 kmph then time taken by the car to cover the distance is:
a. 8
b. 9
c. 4
d. 6

Answer: C
Explanation:
$D = S \times T$ $ \Rightarrow S \propto \dfrac{1}{T}$ ($\because $ Distance is constant)
$ \Rightarrow ST = K$
$ \Rightarrow {S_1}{T_1} = {S_2}{T_2}$
$ \Rightarrow 40 \times 5 = 50 \times {T_2}$
$ \Rightarrow {T_2} = 4$

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Ratio and Proportion: FormulasRatio and Proportion: Exercise - 1Ratio and Proportion: Exercise - 2