Solution:-

Let us assume the total savings be y.

From the question it is given that,

Vijay kumar invested $10%$, $30%$ and $40%$ of his savings in buying shares of $3$ different companies A, B and C.

Companies A, B and C which declared dividends of $12%$, $15%$ and $16%$ respectively.

Then,

Investment in company X$=10%$ of y $=(10/100)×y$

$= y/10$

Investment in company Y $=30$% of y $=(30/100)×y$

$= (3/10)×y$

$= 3y/10$

Investment in company Z$=40%$ of y $=(40/100)×y$

$= 4/10×$ y

$= 2y/5$

Now,

Dividend given by company X $=12%$ of $y/10$

$= (12 × y)/(100×10)$

$= 0.012y$ … [1]

Dividend given by company Y $= 15%$ of $3y/10$

$= (15×3y)/(100×10)$

$= 0.045$y … [2]

Dividend given by company Z $=16%$ of $2y/5$

$= (16×2y)/(100×5)$

$= 0.064$y … [3]

Given, sum of $1$, $2$ and $3$ is equal to ₹ $3,025$

So, $1+2+3=$ ₹ $3,025$

$0.012y+0.045y+0.064y=3,025$

$Y(0.012+0.045+0.064)=3,025$

$0.121y=3,025$

$Y=25,000$

Therefore, vijay’s savings $=25,000$

Investment in company $X=(y/10)=25,000/10$

$= ₹ 2,500$

Investment in company Y $= (3y/10)$ = $75,000/10$

$= ₹ 7,5004$

Investment in company Z $= (2y/10)$ = $50,000/5$

$= ₹ 10,000$