# Q. 3.     Are the following statements true?             (a) $\inline 40$ persons : $\inline 200$ persons = $\inline Rs.15:Rs.75$             (b) $\inline 7.5$ litres : $\inline 15$ litres = $\inline 5\; kg:10\; kg$             (c) $\inline 99\; kg:45\; kg$  = $\inline Rs.44\; :Rs.\; 20$             (d) $\inline 32\; m:64\; m=6\; sec:12\; sec$            (e) $\inline 45\; km:60\; km=$  $\inline 12$ hours :$\inline 15$ hours

(a) $\inline 40$ persons : $\inline 200$ persons = $\inline Rs.15:Rs.75$

$\frac{40}{200}=\frac{1}{5}.........(1)$

$\frac{15}{75}=\frac{1}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(b) $\inline 7.5$ litres : $\inline 15$ litres = $\inline 5\; kg:10\; kg$

$\frac{7.5}{15}=\frac{1}{2}.........(1)$

$\frac{5}{10}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(c) $\inline 99\; kg:45\; kg$  = $\inline Rs.44\; :Rs.\; 20$

$\frac{99}{45}=\frac{11}{5}.........(1)$

$\frac{44}{20}=\frac{11}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(d) $\inline 32\; m:64\; m=6\; sec:12\; sec$

$\frac{32}{64}=\frac{1}{2}.........(1)$

$\frac{6}{12}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(e) $\inline 45\; km:60\; km=$  $\inline 12$ hours :$\inline 15$ hours

$\frac{45}{60}=\frac{3}{4}.........(1)$

$\frac{12}{15}=\frac{4}{5}.........(2)$

As we can see (1) is not equal to (2), They are not in proportion.

Hence the statement is False.

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