Question

A sum of rs 105 is divided into two parts. if two times the greater part is 15 less than three times the smaller part, find the parts of the sum.​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Rs. 105 is divided into Rs. 60 and Rs. 45

$\mathfrak{\large{\underline{\underline{Explanation :- }}}}$

Given :

Total Amount - Rs. 105

Two times the Greater part is = 15 less than three times the smaller part

To Find :

Parts of the sum

Solution :

◆ $\textbf{\small{\underline{Consider the -}}}$

• Greater part as x
• Smaller part as (105 - x)

◆ $\textbf{\small{\underline{According to the Question -}}}$

Two times the greater part is = 15 less than three times the smaller part

★ $\boxed{\sf{2x=3(105-x)-15}}$

$\longrightarrow \: 2x = 3(105 - x) - 15$

$\longrightarrow \: 2x = 315 - 3x - 15$

$\longrightarrow \: 2x + 3x = 315 - 15$

$\longrightarrow \: 5x = 300$

$\longrightarrow \: x = \dfrac{300}{5}$

$\longrightarrow \: x = 60$

Greater part = 60

$\rule{300}{1.5}$

★ Value of (105 - x)

$\longrightarrow \: 105 - 60$

$\longrightarrow \: 45$

Smaller part = 45

$\therefore$ Rs. 105 is divided into Rs. 60 and Rs. 45

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\longrightarrow \: 2(60) =3(45) - 15$

$\longrightarrow \: 120 = 135 - 15$

$\longrightarrow \: 120 = 120$

$\therefore$ Rs. 105 is divided into Rs. 60 and Rs. 45

Answer 2

♋YOUR ANSWERS♍

✍ The money is divided into 60 and 45 rupees

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EXPLANATION —

Given-

》Total amounts of money = rs 105

》The division of money should be 2 times the greater part is 15 less than 3 times the smaller part

To find-

●The parts of the sum = ?

-------------------------------------------

Let consider greater part be x

Then the smaller part be = 105 - x

A/q

》 2x = 3(105-x) - 15

⇒ 2x = 315 - 3x - 15

⇒ 5x = 300

⇒ x = 60

Therefore,

The greater part = x = 60 rupees

The smaller part = 105 - 60 =45 rupees

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