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Ratio
Question 121 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If A : B = 1/2 : 1/3 and B : C = 1/2 : 1/3, then A, B, C is equal to -
3 : 2 : 6 | |
2 : 2 : 3 | |
1 : 2 : 6 | |
9 : 6 : 4 |
Question 121 Explanation:
\begin{align} & = A:B = \frac{1}{2}:\frac{1}{3} = 3:2, \cr & = {\text{B}}:{\text{C}} = \frac{1}{2}:\frac{1}{3} = 3:2 \cr & = \left( {3 \times \frac{2}{3}} \right):\left( {2 \times \frac{2}{3}} \right) \cr & = 2:\frac{4}{3}. \cr & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}} = 3:2:\frac{4}{3} \cr & = 9:6:4. \cr\end{align}
Question 122 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The present ratio of ages of A and B is 4:5. 18 years ago, this ratio was 11:16. Find the sum total of their present ages.
90 years | |
105 years | |
80 years | |
110 years |
Question 122 Explanation:
Let present age of A and B be 4x and 5x.
18 years ago their ages;
(4x-18)/(5x-18) = 11/16;
Or, 64x-288 = 55x-198;
Or, 64x-55x = -198+288;
Or, 9x = 90;
Or, x = 90/9 = 10;
Sum of the present ages = 40+50 = 90 years.
Question 123 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
What is the ratio in Rs. 2.80 and 40 paise?
1 : 14 | |
7 : 1 | |
2 : 7 | |
1 : 7 |
Question 123 Explanation:
Rs. 2.80 = 280 paise
∴ Required ration = 280 : 40
=7 : 1
Question 124 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
${\text{If }}\frac{a}{b} = \frac{b}{c} = \frac{c}{d}, {\text{then}}$ $\frac{{{b^3} + {c^3} + {d^3}}}{{{a^3} + {b^3} + {c^3}}}{\text{will be equal to - }}$
d/a | |
b/c | |
c/d | |
a/b |
Question 124 Explanation:
\begin{align} & {\text{Let }}\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = k \cr & {\text{Then, }} \cr & a = bk, \cr & b = ck, \cr & c = dk. \cr & {\text{Also, }} \cr & \Rightarrow \frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} = {k^3} \cr & \Rightarrow {k^3} = \frac{a}{{d.}} \cr & \therefore \frac{{{b^3} + {c^3} + {d^3}}}{{{a^3} + {b^3} + {c^3}}} \cr & = \frac{{{b^3} + {c^3} + {d^3}}}{{{{\left( {bk} \right)}^3} + {{\left( {ck} \right)}^3} + {{\left( {dk} \right)}^3}}} \cr & = \frac{{{b^3} + {c^3} + {d^3}}}{{{k^3}\left( {{b^3} + {c^3} + {d^3}} \right)}} \cr & = \frac{1}{{{k^3}}} \cr & = \frac{d}{a}. \cr\end{align}
Question 125 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A sum of Rs. 53 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their share is gets. The ratio of their share is =?
18 : 25 : 10 | |
16 : 9 : 18 | |
15 : 8 : 30 | |
25 : 28 : 10 |
Question 125 Explanation:
\begin{align} & {\text{Let C gets }}x{\text{ rupees}} \cr & \therefore {\text{B gets }}x + 8{\text{ rupees}} \cr & \therefore {\text{A gets }}x + 8 + 7{\text{ rupees}} \cr & {\text{Total A}} + {\text{B}} + {\text{C}} \cr & \Rightarrow x + 15 + x + 8 + x = 3x + 23 \cr & \Rightarrow 3x + 23 = {\text{Rs}}{\text{. }}53({\text{given)}} \cr & \Rightarrow 3x = 30 \cr & \Rightarrow x = 10 \cr & \Rightarrow x = {\text{Rs}}{\text{.10}} \cr & \therefore {\text{Ratio of their shares is }} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, {\text{A}}\, \, \, \, \, \, \, \, \, :\, \, \, \, \, \, {\text{B}}\, \, \, \, \, \, \, \, :\, \, \, {\text{C}} \cr & {\text{ = }}\left( {x + 15} \right):\left( {x + 8} \right):\left( x \right) \cr & = \, \, \, \, \, \, \, \, \, 25\, \, \, \, \, \, \, \, \, :\, \, \, \, \, \, \, 18\, \, \, \, \, :\, \, 10 \cr\end{align}
There are 125 questions to complete.