1. If $A:B = 3 : 4$ and $B:C = 4 : 7$ then $A:C=?$
a. 7 : 3
b. 4 : 7
c. 3 : 7
d. 7 : 11

Answer: C

Explanation:
Given that, $A:B = 3: 4$ and $B : C = 4 :7$
Now, the values of $B$ in both the ratios are equal.
$\begin{array}{cc}
A:\boxed{B} & = 3: \boxed4 \\
\boxed{B}:C & = \boxed4 : 7 \\\hline
A : C &= 3 : 7
\end{array}$

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2. If $A:B = 3 : 8$ and $B:C = 4 : 7$ then $A:C=?$
a. 7 : 3
b. 14 : 3
c. 3 : 7
d. 3 : 14

Answer: D

Explanation:
Given that, $A:B = 3: 8$ and $B : C = 4 :7$
Now, the values of $b$ in both the ratios are not equal. So we have to equate them by multiplying with suitable integer.
$\begin{array}{cl}
A:{B} & = (3: 8) \\
{B}:C & = (4 : 7)\times 2 &= 8 : 14 \\
\end{array}$
$\therefore$ $A : C = 3 : 14$

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3. If $A:B = 3 : 4$ and $B:C = 5 : 7$ then $A:C=?$
a. 7 : 3
b. 14 : 3
c. 15 : 28
d. 3 : 7

Answer: C

Explanation:
Given that, $A:B = 3: 4$ and $B: C = 5 :7$
Now, the values of $b$ in both the ratios are not equal. So we have to equate them by multiplying with suitable integers.
$\begin{array}{cl}
A:{B} & = (3: 4) \times 5 &= 15 : 20 \\
{B}:C & = (5 : 7)\times 4 &= 20 : 28 \\
\end{array}$
$\therefore$ $A : C = 15 : 28$

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4. If $A:B = 5 : 6$ and $B: C = 4 : 7$ then $A:C=?$
a. 7 : 3
b. 15 : 21
c. 10 : 21
d. 5 : 14

Answer: C

Explanation:
Given that, $a:b = 5: 6$ and $b : c = 4 :7$
Now, the values of $b$ in both the ratios are not equal. So we have to equate them by multiplying with suitable integers.
$\begin{array}{cl}
A:{B} & = (5: 6) \times 2 &= 10 : 12 \\
{B}:C & = (4 : 7)\times 3 &= 12 : 21 \\
\end{array}$
$\therefore$ $A : C = 10 : 21$

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5. If $A: B = 2 : 3$, $B : C = 4 : 5$, $C : D = 5 : 2$, then $A : D=?$
a. 9 : 6
b. 6 : 9
c. 3 : 4
d. 4 : 3

Answer: D

Explanation:
$\begin{array}{cl}
A:{B} & = (2: 3) \times 4 &= 8 : 12 \\
{B}:C & = (4 : 5)\times 3 &= 12 : 15 \\
\end{array}$
$A : B : C = 8 :12: 15$ and $C : D = 3 : 2$
Now let us equate $c$ in both the ratios.
$\begin{array}{rll}
A:B :C & = (8:12:15) & &= 8 : 12 :15 \\
C:D & = (5 : 2) &\times 3 &= 15 : 6 \\
\end{array}$
$A : B : C : D = 8 : 12 : 15 : 6$
$\therefore$ $A : D = 8 : 6 = 4 : 3$

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6. $A$'s money is to $B$'s money as $4:5$ and $B$'s money is to $C$'s money as $2:3$. If A has $\text{Rs}.800$, $C$ has
a. Rs.1000
b. Rs.1200
c. Rs.1500
d. Rs.2000

Answer: C

Explanation:
$\begin{array}{rll}
A : B & = (4 : 5) &\times 2 &= 8 : 10 \\
B : C & = (2 : 3) &\times 5 &= 10 : 15 \\
\end{array}$
($\because$ As $B$ is common in both the ratios, we have to multiply these two ratios with suitable numbers to make $B$ equal)
$A:B:C = 8 : 10 : 15$
Let $A, B, C = 8x, 10x, 15x$
Given $8x = 800$ $\Rightarrow $ $x = 100$
$C = 15x = 15×100 = \text{Rs}.1500$

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7. A certain amount was divided between Kavita and Reena in the ratio of $4:3$. If Reena's share was $\text{Rs}.2400$, the amount is :
a. Rs. 5600
b. Rs. 3200
c. Rs. 9600
d. Rs. 9800

Answer: A

Explanation:
Let their shares be $\text{Rs}.4x$ and $\text{Rs}.3x$.
Thus, $3x = 2400$ $ \Rightarrow x = 800$
Total amount $= 4x + 3x = 7x = \text{Rs}.5600$

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8. The prices of a scooter and a television set are in the ratio 3:2 . If a scooter costs Rs.6000 more than the television set, the price of the television set is :
a. Rs.6000
b. Rs.10,000
c. Rs.12,000
d. Rs.18,000

Answer: C

Explanation:
Let the price of scooter be $Rs.3x$ and that of a television set be $Rs.2x$
Then $3x - 2x = 6000$ or $x = 6000$
Cost of a television set $ =2x = \text{Rs}.12000$