Question

Three numbers are in ratio 2:3:5. If the sum of the largest and the smallest equals the sum of the third is 32, find the numbers ?​

Answer 1

▄︻デANSWER══━一 ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎⁍ ‎ ‎

Let ,

the three numbers in the ratio 2:3:4 be 2x, 3x and x respectively

obviously the largest and smallest numbers will be 5x and 2x respectively.

according to the question,

5x + 2x = 3x + 32

⇒7x = 3x +32

⇒7x - 3x = 32

⇒ 4x = 32

⇒x = 32/4

⇒x = 8

the three numbers are,

2x = 2× 8 = 16

3x = 3 × 8= 24

5x = 5× 8= 40

Answer 2

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

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.