Question

Two numbers are in the ratio 2:3 and the product of hcf & lcm is 150 then find the sum of the numbers​

Answer 1

Answer:

★ Numbers = 10 & 15 ★

★ Sum = 10+15 = 25 ★

Step-by-step explanation:

Given:

• Two numbers are in ratio 2:3
• Product of HCF & LCM is 150

To Find:

• What are the numbers and their sum?

Solution: Let x be the common in given ratio

∴ Ratio will be 2x & 3x

• First number = 2x [ n¹ ]
• Second Number = 3x [ n² ]

A/q

$\small\implies{\sf }$ n¹ x n² = HCF x LCM

$\small\implies{\sf }$ 2x(3x) = 150

$\small\implies{\sf }$ 6x² = 150

$\small\implies{\sf }$ x² = 150/6

$\small\implies{\sf }$ x² = 25

$\small\implies{\sf }$ x = √25

$\small\implies{\sf }$ x = 5

Hence, The numbers will be :

• 2x = 2(5) = 10
• 3x = 3(5) = 15

Now Finding the sum of these two numbers

$\small\implies{\sf }$ n¹ + n²

$\small\implies{\sf }$ 2x + 3x

$\small\implies{\sf }$ 5x

$\small\implies{\sf }$ 5(5)

$\small\implies{\sf }$ 25

Hence, Sum of numbers is 25

Answer 2

AnswEr :

$\frak{Given}\begin{cases}\sf{Ratio \: of \: no.s = 2:3}\\\sf{H.C.F \times\ L.C.M = 150}\end{cases}$

$\rule{150}2$

$\normalsize\bullet\:\sf\ Let \: the \: first \: number \: be \: 2x$

$\normalsize\bullet\:\sf\ Let \: the \: second \: number \: be \: 3x$

$\underline{\bigstar\:\textsf{According \: to \: the \: question \: now:}}$

$\normalsize\ : \implies\sf\ Product \: of \: two \: no.s = H.C.F \times\ L.C.M$

$\normalsize\ : \implies\quad\sf\ 2x \times\ 3x = 150$

$\normalsize\ : \implies\quad\sf\ 6x^2 = 150$

$\normalsize\ : \implies\quad\sf\ x^2 = \frac{\cancel{150}}{\cancel{6}}$

$\normalsize\ : \implies\quad\sf\ 2x \times\ 3x = 150$

$\normalsize\ : \implies\quad\sf\ x^2 = 25$

$\normalsize\ : \implies\quad\sf\ x = \sqrt{25}$

$\normalsize\ : \implies\quad{\boxed{\sf{ x = 5 }}}$

$\underline{\bigstar\:\textsf{Sum \: of \: both \: numbers:}}$

$\bf{First \: no.}\begin{cases}\sf{2x = 2 \times\ 5}\\\sf{2x = 10}\end{cases}$

$\bf{Second \: no.}\begin{cases}\sf{3x = 3 \times\ 5}\\\sf{3x = 15}\end{cases}$

$\normalsize\dashrightarrow\sf\ Sum \: of \: two \: numbers = First \: no. + Second \: no.$

$\normalsize\dashrightarrow\quad\sf\ Sum = 10 + 15$

$\normalsize\dashrightarrow\quad\sf\ Sum = 25$

$\normalsize\dashrightarrow\quad{\boxed{\sf \red{Sum = 25}}}$

$\therefore\:\underline{\textsf{Hence, \: the \: sum \: of \: two \: numbers \: is}{\textbf{\: 25}}}$