Question

Three. numbers are in ratio 2:3.4. If the sum of the largest and the smallest equals the Sum of the third is 33, find the numbers​

Answer 1

Answer :-

The numbers are 11, 22 and 16.5 .

EXPLANATION

To Find :-

• The numbers.

★ Solution

Given that,

• Three numbers are in the ratio 2:3:4
• Sum of largest and smallest 33.

ㅤㅤㅤ✧ㅤAssumption ㅤ✧

Let us assume the numbers as "2n", "3n" and "4n".

ㅤ∴ 2n + 4n = 33 .... given

→ 2n + 4n = 33

→ 6n = 33

→ n = 33/6

→ n = 5.5

The value of n is 5.5 .

According the question,

The numbers are :-

• 2n = 2*5.5 = 11
• 3n = 3*5.5 = 16.5
• 4n = 4*5.5 = 22

ㅤㅤ_____________________

Verification

• 2n + 4n = 33

We have,

L.H.S = 2n + 4nㅤandㅤR.H.S = 33

By putting the value of "n" in L.H.S :-

→ 2n + 4n

→ 2*5.5 + 4*5.5

→ 11 + 22

→ 33

Now, L.H.S = R.H.S

Hence, Verified!

Answer 2

Answer:

${\large{\underline{\sf{Solution-}}}}$

Let the numbers be 2x, 4x, 5x

→ Largest number = 5x

→ Smallest Number = 2x

From Question,

${ \longrightarrow{ \sf{2x + 5x = 4x + 33}}}$

${ \longrightarrow{ \sf{7x = 4x + 33}}}$

${ \longrightarrow{ \sf{7x - 4x = 33}}}$

${ \longrightarrow{ \sf{3x = 33}}}$

${ \longrightarrow{ \sf{x = \frac{33}{3} }}}$

${ \longrightarrow{ \pmb{ \sf{x = 11}}}}$

By Substituting,

→ 2x = 2(11) = 22

→ 4x = 4(11) = 44

→ 5x = 5(11) = 55

Verification,

${ \longrightarrow{ \sf{2x + 5x = 33 + 4x}}}$

${ \longrightarrow{ \sf{22 + 55 = 44 + 33}}}$

${ \longrightarrow{ \sf{ \pmb{77 = 77}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \therefore{ \underline{ \pmb{ \rm{ Hence \: Proved}}}}}$

${ \therefore{ \underline{ \pmb{ \rm{The \: Three \: Numbers \: Are \: 22,44,55}}}}}$

Note:-

correct Question:-

Three numbers are in ratio 2:3:4. If the Sum of the largest and the smallest equals the sum of the third is 33, find the numbers.