Question

2. The sum of two numbers is 2000. If 25% of the smaller number is one-sixth of the larger, find the numbers.​

Answer 1

$\large\bf\underline {To \: find:-}$

• We need to find the numbers.

$\large\bf\underline{Given:-}$

• Sum of two numbers is 2000
• 25% of the smaller number is one-sixth of the larger.

$\huge\bf\underline{Solution:-}$

Let the two numbers be x and y

Sum of two numbers is 2000

• x + y = 2000
• x = 2000 - y .....1)

❥ According to question:-

25% of the smaller number is one-sixth of the larger.

• Let x is smaller than y
• x < y

So,

$\large \tt \rightarrowtail \: \frac{25}{100} \times x = \frac{1}{6} \times y$

$\large \tt \rightarrowtail \: \cancel\frac{25x}{100} = \frac{y}{6}$

$\large{ \tt \rightarrowtail \: \frac{x}{4} = \frac{y}{6} }$

$\tt \rightarrowtail \: 6x = 4y$

• Dividing both side by 2

$\tt \rightarrowtail \: 3x = 2y$

$\tt \rightarrowtail \: 3(2000 - y) = 2y$

$\tt \rightarrowtail \: 6000 - 3y = 2y$

$\tt \rightarrowtail \: 5y = 6000$

$\tt \rightarrowtail \: y = \cancel{\frac{6000}{5}}$

$\large\bf \rightarrowtail \: y = 1200$

putting value of y in 1)

↣x = 2000 - y

↣ x = 2000 - 1200

↣ x = 800

Hence,

• ❥ Smallest number = 800
• ❥ Larger number = 1200

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\bf\large{\underline{\underline{Question}}}$

The sum of two numbers is 2000. If 25% of the smaller number is one-sixth of the larger, find the numbers.

$\bf\large{\underline{\underline{Given}}}$

• Sum Of Two Number Is 2000
• 25% Of The Smaller Number Is 1/6 th Of The Larger Number.

$\bf\large{\underline{\underline{To\:Find}}}$

• Number = ?

$\bf\large{\underline{\underline{According\:To\:Question}}}$

• Let the smaller number be x
• And larger number be 2000 - x

$\bf\large{\underline{\underline{Procedure}}}$

$\sf→ 0.25x=\frac{1}{6}(2000-x)\\\sf→ \frac{25}{100}x=\frac{2000}{6}-\frac{x}{6}\\\sf→\frac{1}{4}x=\frac{2000}{6}-\frac{1}{6x}\\\sf→\frac{1}{4x}+\frac{1}{6x}=\frac{2000}{6}\\\sf→ \frac{5}{12}x=\frac{2000}{6}\\\sf→30x=2400\\\sf→ x=\frac{2400}{30}\\\sf{\underline{\fbox{\underline{\green{x=800}}}}}$

$\rule{230}2$

$\bf\large{\underline{\underline{Hence}}}$

• Smaller number = 800
• Larger number = 2000-800 = 1200