Question

Two numbers are in the ratio 11:12 and their sum is 460. Find the numbers? ​

Answer 1

Given :

• Two numbers are in the ratio 11:12 and the sum is 460.

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To Find :

• Find the numbers.

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Solution :

$\color{maroon}{❒}$Let the Ratios :

• ➳ 1st number = 11y
• ➳ 2nd number = 12y

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Calculating the Value of y :

${\longmapsto{\qquad{\sf{ 11y + 12y = 460 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 23y = 460 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ y = \cancel\dfrac{460}{23} }}}} \\ \\ \ {\qquad{\textsf{ Value of y = {\blue{\sf{ 20 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Calculating the Numbers :

$\qquad\large{\orange{\underline{\underline{\red{\sf{ 1st \: Number \: = 11y = 11 \times 20 = 220 }}}}}}$

$\\ \qquad\large{\orange{\underline{\underline{\red{\sf{ 2nd \: Number \: = 12y = 12 \times 20 = 240 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Therefore :

❝ The first number is 220 and the second number is 240 .❞

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Answer 2

$\small\bold\red{Given:-}$

• The ratio of two numbers is 11 : 12.
• Sum of the ratio is 460

$\small\bold\green{To \: Find :-}$

• The Numbers

$\small\bold\pink{Let \: us \: assume :-}$

• First Number be 11x
• Second Number be 12x

$\small\bold\purple{Solution :-}$

According to the question :-

$11x + 12x = 460 \\ 23x = 460 \: \: \: \: \: \: \: \: \: \: \: \\ x = \frac{460}{23} \: \: \: \: \: \: \: \: \: \: \: \: \\ x = 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

• First number = 11x = 11 × 20= 220
• Second number = 12x = 12 × 20 =240