Question

If 3 by 5 of a number exceeds its 2 by 7 bye 44. Find this number

Answer 1

Correct Question :-

If 3/5 of a number exceeds its 2/7 by 44. Find this number.

Answer

The number is 140.

Step-by-step explanation:

To Find :-

• The number.

★ Solution

Given that,

• 3/5 of a number exceeds it's 2/7 by 44.

Let us assume the number as (n),

$\pink{\sf{\therefore \: \: \: \: \dfrac{3}{5}n - \dfrac{2}{7}n = 44}}$

By simplifying,

$\sf{\longrightarrow \: \: \: \: \dfrac{3}{5}n - \dfrac{2}{7}n = 44}$

$\sf{\longrightarrow \: \: \: \: \dfrac{(7 \times 3)n - (5 \times 2)n}{35} = 44}$

$\sf{\longrightarrow \: \: \: \: \dfrac{21n - 10n}{35} = 44}$

By cross-multiplication,

$\sf{\longrightarrow \: \: \: \: 21n - 10n = 44 \times 35}$

$\sf{\longrightarrow \: \: \: \: 21n - 10n = 1540}$

$\sf{\longrightarrow \: \: \: \: 11n = 1540}$

$\sf{\longrightarrow \: \: \: \: n = \dfrac{1540}{11}}$

$\sf{\longrightarrow \: \: \: \: n = \cancel{ \dfrac{1540}{11}}}$

$\sf{\longrightarrow \: \: \: \: n = 140} \: \: \: \: \: \: \bigstar$

Hence,

The required number is 140.

V E R I F I C A T I O N :-

• $\sf{\dfrac{3}{5}n - \dfrac{2}{7}n = 44}$

By putting the value of n and simplifying the L.H.S :-

We got, n = 140

$\sf{\longrightarrow \: \: \: \: \dfrac{3}{5}n - \dfrac{2}{7}n}$

$\sf{\longrightarrow \: \: \: \: \dfrac{3}{5} \times 140 - \dfrac{2}{7} \times 140}$

$\sf{\longrightarrow \: \: \: \: \dfrac{3 \times 140}{5} - \dfrac{2 \times 140}{7}}$

$\sf{\longrightarrow \: \: \: \: \dfrac{3 \times 140}{5} - \dfrac{2 \times 140}{7}}$

$\sf{\longrightarrow \: \: \: \: \dfrac{420}{5} - \dfrac{280}{7}}$

$\sf{\longrightarrow \: \: \: \: \cancel{\dfrac{420}{5}} - \cancel{\dfrac{280}{7}}}$

$\sf{\longrightarrow \: \: \: \: 84 - 40}$

$\sf{\longrightarrow \: \: \: \: 44}$

Now, L.H.S = R.H.S = 44

Hence, Verified!