Question

4. One-fourth of a number is 3 more than one-fifth of its successor. Find the number.
​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• One-fourth of a number is 3 more than one-fifth of its successor

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The number

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

• Let the number be 'z'

$\:\:$

• Then its successor will be 'z + 1'

$\:\:$

$\underline{ \underline{\bold{\texttt{One fourth of the number :}}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 4 } \times z$ ⚊⚊⚊⚊ ⓵

$\:\:$

$\underline{ \underline{\bold{\texttt{One fifth of the successor number :}}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 5 } \times (z + 1)$ ⚊⚊⚊⚊ ⓶

$\:\:$

Given that , One-fourth of a number is 3 more than one-fifth of its successor

$\:\:$

Thus ,

$\:\:$

From equation ⓵ & ⓶

$\:\:$

: ➜ $\sf \dfrac { 1 } { 4 } \times z = \dfrac { 1 } { 5 } (z + 1) + 3$

$\:\:$

: ➜ $\sf \dfrac { z } { 4 } = \dfrac { (z + 1)} { 5 } + 3$

$\:\:$

: ➜ $\sf \dfrac { z } { 4 } = \dfrac { (z + 1 + 15)} { 5 }$

$\:\:$

: ➜ $\sf \dfrac { z } { 4 } = \dfrac { (z + 16)} { 5 }$

$\:\:$

: ➜ 5z = 4(z + 16)

$\:\:$

: ➜ 5z = 4z + 64

$\:\:$

: ➜ 5z - 4z = 64

$\:\:$

: : ➨ z = 64

$\:\:$

• Hence the number is 64