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  • A triangle is formed by X- axis, Y-axis and the line 3x + 4y = 4y = 60. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is<

A triangle is formed by X- axis, Y-axis and the line 3x + 4y = 4y = 60. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is

Option: 1

31


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & 3 x+4 y=60 \\ & x=1,4 y=57, y=14.2 \\ & x=1, y=1,2,3, \ldots \ldots .14 \rightarrow 14 \text { points } \\ & x=2,4 y=54, y=13.5 \\ & x=2, y=2,4,6,8,10,12 \rightarrow 6 \text { points } \\ & x=3, y=3,6,9,12 \rightarrow 4 \text { points } \end{aligned}

\begin{aligned} & x=4, y=4,8 \rightarrow 2 \text { points } \\ & x=5, y=5,10 \rightarrow 2 \text { points } \\ & x=6, y=6 \rightarrow 1 \text { points } \\ & x=7, y=7 \rightarrow 1 \text { points } \\ & x=8, y=8 \rightarrow 1 \text { points } \\ & x=9,4 y=23, y=5.7 \quad \times \text { no point } \\ & \text { Total points }=14+6+4+2+2+1+1+1=31 \end{aligned}

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