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The ratio of the ages of Sachin and Amit is $7: 4$ and the sum of their ages is 33 years, then find the ratio of their ages before 6 years.

(a) $3: 15$

(b) $15: 9$

(c) $2: 5$

(d) $5: 2$

Solution

Let the ages of Sachin and Amit be $7 x$ and $4 x$.

From the question,

\begin{aligned} & 7 x+4 x=33 \\ \Rightarrow & 11 x=33 \\ \therefore \quad & x=\frac{33}{11}=3 \text { years } \end{aligned}

Now, the Age of Sachin $=7 x$

\begin{aligned} &=7 \times 3 \\ &=21 \text { years } \\ \& \text { the age of Amit } &=4 \times \\ &=4 \times 3 \\ &=12 \text { years } \end{aligned}

$$\text { Befor } 6 \text { years their ages will be }$$

$21-6=15$ years $\& 12-6=6$ years

$\therefore \quad$ Ratio $=\frac{15}{6}=\frac{5}{2}=5: 2 ;$ Ans.

$\therefore \quad$ Correct option is $(\mathrm{d})$

Trick :

Sachin : Amit

$$\begin{array}{l} \quad 7 \quad: 4 \\ \Rightarrow \quad: 7+4=33 \\ \Rightarrow \quad 1=3 \\ \Rightarrow \quad: 2=6 \\ \therefore \quad \text { After } 6 \text { years the required } \\ \text { Patio }=(7-2):(4-2)=5: 2 ; \text { Ans. } \end{array}$$

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