Sarthaks Test
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Complete the following tables given that x varies directly as y.

(i)

X2.5................15
Y5812..........

(ii)

X5........103525.........
Y812............................32

(iii)

X6810........20
Y1520..........40.............

1 Answer

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Best answer

(i) 

X2.54615
Y581230

\(\frac{2.5}{5}\) = \(\frac{x_1}{8}\)

On cross multiplication, we get

2.5 x 8 = x1 x 5

x1 = \(\frac{2.5\times 8}{5}\) = 4

\(\frac{4}{8}\) = \(\frac{x_2}{12}\)

On cross multiplication, we get

4 x 12 = 8 x x2

\(\frac{48}{8}\) = x2

6 = x2

\(\frac{6}{12}\) = \(\frac{15}{x_3}\)

On cross multiplication, we get

15 x 12 = 6 x x3

\(\frac{180}{6}\) = x3

30 = x3

(ii) 

X57.510352520
Y81216564032

\(\frac{5}{8}\) = \(\frac{x_1}{12}\)

On cross multiplication, we get

 5 x 12 = x1 x 8

x1 = \(\frac{5\times 12}{8}\) = 7.5

\(\frac{7.5}{12}\) = \(\frac{10}{x_2}\)

On cross multiplication, we get

10 x 12 = 7.5 x x2

\(\frac{120}{7.5}\) = x2

16 = x2

\(\frac{10}{16}\) = \(\frac{35}{x_3}\)

On cross multiplication, we get

16 x 35 = 10 x x3

\(\frac{16\times 35}{10}\) = x3

56 = x3

\(\frac{35}{56}\) = \(\frac{25}{x_4}\)

On cross multiplication, we get

56 x 25 = 35 x x4

40 = x4

\(\frac{25}{40}\) = \(\frac{x_5}{32}\)

On cross multiplication, we get

25 x 32 = 40 x x5

\(\frac{25\times 32}{40}\) = x5
20 = x5

(iii) 

X68101620
Y1520254050

\(\frac{8}{20}\)\(\frac{10}{x_1}\)

On cross multiplication, we get

10 x 20 = x1 x 8

x1 = \(\frac{10\times 20}{8}\) = 25

\(\frac{10}{25}\) = \(\frac{x_2}{40}\)

On cross multiplication, we get

10 x 40 = 25 x x2

\(\frac{400}{25}\) = x2

16 = x2

\(\frac{16}{40}\) = \(\frac{20}{x_3}\)

On cross multiplication, we get

20 x 40 = 16 x x3

\(\frac{20\times 40}{16}\) = x3

50 = x3

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