Question

Two numbers having 3 digits are in the ratio 3 : 4. If 20 is added to a smaller
number and 40 is substracted from greater number their ratio becomes 5:6.
Then what is the half of the smaller number?
(1) 240
(2) 480
(3) 320
(4) 120​

Answer 1

Answer:

Option (1)

Step-by-step explanation:

As per the provided question, we have :

• Two numbers having 3 digits are in the ratio 3 : 4.
• If 20 is added to a smaller number and 40 is substracted from greater number their ratio becomes 5:6.

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We are asked to find the half of the smaller number.

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Let us assume the numbers as 3x and 4x respectively.

Here,

• 3x ⇒ Smaller number
• 4x ⇒ Greater number

$\longmapsto \sf {Half_{(Smaller \; Number)} = \dfrac{3x}{2} }$

Let it be the equation (1).

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Finding value of x :

According to the question,

• If 20 is added to a smaller number and 40 is substracted from greater number their ratio becomes 5:6.

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$\longrightarrow \sf {\dfrac{3x + 20}{4x - 40} = \dfrac{5}{6} }$

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$\longrightarrow \sf {6(3x + 20)= 5(4x - 40)}$

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$\longrightarrow \sf {18x + 120= 20x - 200}$

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$\longrightarrow \sf {120 + 200= 20x - 18x}$

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$\longrightarrow \sf {320 = 2x}$

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$\longrightarrow \sf { \dfrac{320}{2} = x}$

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$\longrightarrow \sf {160 = x}$

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Substituting the value of x in the equation (1).

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$\longmapsto \sf {Half_{(Smaller \; Number)} = \dfrac{3x}{2} }$

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$\longmapsto \sf {Half_{(Smaller \; Number)} = \dfrac{3(160)}{2} }$

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$\longmapsto \sf {Half_{(Smaller \; Number)} = \dfrac{480}{2} }$

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$\longmapsto \boxed{\sf {Half_{(Smaller \; Number)} = 240}}$

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Therefore, half of the smaller number is 240.