Question

1. The sum of two numbers is 4980. If 13% of the one number is equal to 17% of the other. Find thenumber.

Answer 1

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

• Sum of two numbers = 4980
• 13% of one number is equal to the 17% of the other number

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

• Numbers

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

Let x and y be the two numbers

▶️ According to Question:--

✥ Sum of two numbers = 4980

≫ x + y = 4980

• ≫ x = 4980 - y .......(1)

✥ 13% of the one number is equal to 17% of the other.

[13% of a number mean 13/100 of the number ]

[ 17% of a number means 17/100 of the number]

• ≫ 13x = 17y......(2)

✥Substituting value of x From (1) in (2)

≫ 13(4980 - y) = 17y

≫ 64740 - 13y = 17y

≫ 64740 = 17y + 13y

≫ 64740 = 30y

≫ y = 64740/30

• ≫ y = 2158

✥ putting value of y in (1)

≫ x = 4980 - 2158

• ≫ x = 2822

Hence,

✝️ Two numbers are 2158 and 2822.

$\rule{200}3$

Answer 2

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

▪The sum of two numbers is 4980.

▪13% of the one number is equal to 17% of the other.

$\red{\bf{\underline{To\:Find:-}}}$

▪The two numbers

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

Let the two number be 'a' and 'b'.

According to the 1ˢᵗ condition,

$\bold{a +b= 4980}$

$⟹a = 4980 - b.........(i)$

According to the 2ⁿᵈ condition,

13% of a = 17% of b

$⟹\bold{ \frac{13}{100} \times a = \frac{17}{100} \times b }.......(ii)$

$⟹ \frac{13a}{100} = \frac{17b}{100}$

$⟹13a = 17b$

$⟹13 \times (4980 - b) = 17b$

$⟹64740 - 13b= 17b$

$⟹64740 = 17b + 13b$

$⟹30b = 64740$

$⟹b = \frac{64740}{30}$

$\bold{∴b = 2158}$

Now,

$a + b = 4980$

$⟹a + 2158 = 4980$

$⟹a = 4980 - 2158$

$\bold{∴a = 2822}$

$\bold\pink{\boxed{Therefore,\:the\:two\:numbers\:are\:2822\:and\:2158}}$

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Hope It Helps Uh! ❤