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Ratio
Question 91 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If a : b = c : d, then $\frac{{{\text{ma + nc}}}}{{{\text{mb + nd}}}}{\text{ is equal to - }}$
m : n | |
a : b | |
dm : cn | |
an : mb |
Question 91 Explanation:
\begin{align} & {\text{Let }}\frac{a}{b} = \frac{c}{d} = k. \cr & {\text{Then, }} \cr & \Rightarrow a = bk, \, c = dk. \cr & \therefore \frac{{ma + nc}}{{mb + nd}} \cr & = \frac{{mbk + ndk}}{{mb + nd}} \cr & = \frac{{k\left( {mb + nd} \right)}}{{\left( {mb + nd} \right)}} \cr & \Rightarrow k = \frac{a}{b} \cr & \Rightarrow a:b \cr\end{align}
Question 92 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
\begin{align} & {\text{The value of }}x{\text{ where}} \cr & x:2\frac{1}{3}::21:50\, {\text{is}} - \cr\end{align}
11/50 | |
11/49 | |
27/50 | |
49/50 |
Question 92 Explanation:
\begin{align} & = x:2\frac{1}{3}::21:50 \cr & \Rightarrow 50x = \frac{7}{3} \times 21 \cr & = 49 \cr & \Rightarrow x = \frac{{49}}{{50}} \cr\end{align}
Question 93 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes
4:3 | |
10:7 | |
8:7 | |
12:7 |
Question 93 Explanation:
Boys: girls = 8:5; (let the boys = 8x; girl = 5x)
Total strength = 286;
8x+5x = 286;
13x = 286;
Or, x = 286/13 = 22;
Boys = 176 and girls = 110;
22 more girls get admitted then number of girls become,
(5x+22) = 110+22 = 132;
Now, new ratio of boys and girls = 176:132 = 4:3.
Question 94 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Rs. 600 are divided among A, B, C so that Rs. 40 more than 2/5 of A's share, Rs. 20 more than 2/7 of B's share and Rs. 10 more than 9/17 of C's share may all be equal. What is A's share?
Rs. 170 | |
Rs. 280 | |
Rs. 200 | |
Rs. 150 |
Question 94 Explanation:
\begin{align} & = \frac{2}{5}{\text{A}} + 40 = \frac{2}{7}{\text{B}} + 20 \cr & \Rightarrow \frac{2}{7}{\text{B}} = \frac{2}{5}{\text{A}} + 20 \cr & \Rightarrow {\text{B}} = \frac{7}{2}\left( {\frac{2}{5}{\text{A}} + 20} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = \left( {\frac{7}{5}{\text{A}} + 70} \right). \cr & {\text{And, }} \cr & = \frac{2}{5}{\text{A}} + 40 = \frac{9}{{17}}{\text{C}} + 10 \cr & \Rightarrow \frac{9}{{17}}{\text{C}} = \frac{2}{5}{\text{A}} + 30 \cr & \Rightarrow {\text{C}} = \frac{{17}}{9}\left( {\frac{2}{5}{\text{A}} + 30} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3}. \cr & = {\text{A}} + {\text{B}} + {\text{C}} = 600 \cr & \Rightarrow {\text{A}} + \left( {\frac{7}{5}{\text{A}} + 70} \right) + \left( {\frac{{34}}{{45}}{\text{A}} + \frac{{170}}{3}} \right) = 600 \cr & \Rightarrow \frac{{142{\text{A}}}}{{45}} = 600 - \frac{{380}}{3} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{1420}}{3} \cr & \Rightarrow {\text{A}} = \frac{{1420}}{3} \times \frac{{45}}{{142}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 150. \cr\end{align}
Question 95 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is
15 | |
36 | |
9 | |
45 |
Question 95 Explanation:
Let two numbers be 4x and 5x;
their LCM = 180 and HCF = x; Now,
1st number * 2nd number = LCM*HCF
Or, 4x*5x = 180*x;
Or, 20x = 180;
Or, x = 9;
then, the smaller number = 4*9 = 36.
There are 95 questions to complete.