Ratio Questions and Answers

$text{Share of C} = 1-frac{5}{16}-frac{7}{12}=frac{5}{48}$

 $= frac{1}{2}:frac{2}{3}:frac{3}{4}$

or 

$frac{1}{2} times12:frac{2}{3}times12:frac{3}{4}times12=6:8:9$

$therefore text{ parts are}$

$frac{6}{6+8+9}times391=102 ,$

$frac{8}{6+8+9}times391=136$

$text{and}$

$frac{9}{6+8+9}times391=153$

$=x + y = 20$

$=x - y = 2.5$

$text{Find } x text{ and } y$

$= 6 : 8 = 9 : x$

$= 6x = 72$

$= x = frac{72}{6}$

$x = 12$
 

$=frac{2}{3}times 1260 : 0.6 times 2100 = 2:3$

$text{ First part } = frac{2}{2+7} times 225 = 50$

$text{ Second part } = frac{7}{2+7} times 225 = 175$

$=x times 0.7 = y times 0.05$

$therefore frac{x}{y} = frac{.75}{.7} = frac{75}{700} = frac{3}{28}$

$5x + 11(37 - x) = 227$

$therefore x = 30 text{ and the other part is } 7$

Total value of one group of 5 coins of 50 P,
6 coins of 25 P and
2 coins of one rupee = Rs. 2.50 + Rs. 1.50 + Rs. 2.00 = Rs. 6.00

Since the total value is Rs. 42; So there are 7 such groups.

The number of 25 P coins = 7 $times$ 6 = 42

Check from choice

$9 : 12 Rightarrow 3 : 7 text{ true}$

$(9 + 6) : (21 + 6) = 15 : 27 Rightarrow 5 : 9 text{ true}$

Number of teachers $= frac{3}{28} times 896 = 96$

$= frac{10}{100} x = frac{20}{100}y Rightarrow frac{x}{y} = frac{2}{1}$

Let ratio be $x$

then 1st no. be $x$

2nd no. be $5x$

$therefore x times 5x = 320$

$therefore x = 8$

Numbers are 8, 40

$therefore text{ Difference } = 40^2 - 8^2 = 1536$

Since, $4x + 3:9x + 10$ is the triplicate ratio of 3 : 4.

$begin{aligned} & text{Therefore, } frac{4x + 3}{9x + 10} = frac{3}{4} times frac{3}{4} times frac{3}{4} \ &Rightarrow frac{4x + 3}{9x + 10} = frac{27}{64} \ &Rightarrow 64(4x + 3) = 27(9x + 10) \ &Rightarrow 256x + 192 = 243x + 270 \ &Rightarrow 256x - 243x =270-192 \ &Rightarrow 13x = 78 \ &therefore x = frac{78}{13} \ &=6 end{aligned}$

The duplicate ratio of $5 : 6 text{ is } dfrac{5}{6} times dfrac{5}{6} = dfrac{25}{36}$

The reciprocal ratio of $25 : 42 text{ is } dfrac{1}{25} times dfrac{1}{42} text{ i.e. } dfrac{42}{25}$

and sub duplicate ratio of $dfrac{36}{49}$ $36 : 49 text{ is } dfrac{sqrt{36}}{sqrt{49}} = dfrac{6}{7}$
$\text{is }\genfrac{}{}{0ex}{}{\sqrt{36}}{\sqrt{49}}=\genfrac{}{}{0ex}{}{6}{7}$

 $therefore$ Compound ratio is $dfrac{25}{36} times dfrac{42}{25} times dfrac{6}{7} = dfrac{1}{1} = 1:1$

The required compounded ratio is

$dfrac{2a}{6b} times dfrac{7a}{49b} times dfrac{3a}{12b} = dfrac{a^3}{84b^3} = a^3 : 84b^3$

$begin{aligned} & text{Duplicate ratio of } 5:8 = dfrac{5^2}{8^2} \ & Rightarrow dfrac{5^2}{8^2} = dfrac{x+5}{3x+4} \ & Rightarrow dfrac{25}{64} = dfrac{x+5}{3x+4} \ & Rightarrow 25(3x+4) = 64(x+5) \ & Rightarrow 75x+100 = 64x+320 \ & Rightarrow 75x-64x = 320-100 \ & Rightarrow 11x=220 \ & therefore x = dfrac{220}{11} = 20 end{aligned}$

The mean proportional between $(2 + sqrt{3})$ and $(8 - sqrt{48})$

$begin{aligned} &=sqrt{(2+sqrt{3}) (8-sqrt{48})} \ &=sqrt{(2+sqrt{3}) 4(2-sqrt{3})} \ &=2sqrt{(2+sqrt{3}) (2-sqrt{3})} \ &=2sqrt{(4-sqrt{3})} = 2times 1 = 2 \ &[because (a-b)(a+b) = a^2 - b^2] end{aligned}$

Let the consequent be $x$.

$therefore 35:x = 7:8$

Then, $dfrac{35}{x} = dfrac{7}{8}$

$begin{aligned} &Rightarrow 7x = 35 times 8 \ &therefore x = dfrac{35 times 8}{7} = 40 end{aligned}$