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.
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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) $5: 2$

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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 $=7 x$

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

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

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

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

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

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