Question

(18. The sum of two numbers is 80. If the larger number exceeds four
times the smaller one by 5, then the smaller number is :
अगर दो संख्याओं का योग 80 है, तथा बड़ी वाली संख्या, छोटी संख्या 5 से ।
चार गुना बड़ी संख्या है, तो छोटी संख्या होगी ।
(1) 5 (2) 15 (3) 20 (4) 25
​

Answer 1

Let x and y be the two numbers. And x > y.

Then,

x + y = 80

Also,

x = 4y - 5

Solving the two equations,

80 - y = 4y - 5

75 = 5y

Therefore, y = 15.

Hope this helps you.

Answer 2

$\underline{\underline{\sf{Answer}}}$

Option 2) i.e. 15 is the right answer.

$\huge\bold{Explanation}$

$\underline{\underline{\sf{Given}}}$

Sum of two numbers = 80.

दो संख्याओं का योग 80 है I

$\underline{\underline{\sf{To\:Find}}}$

The smaller number = ?

छोटी संख्या = ??

$\sf{Let\:the\:first\:number\:be\:x}$

$\sf{Let\:the\:second\:number\:be\:80-x}$

$\bold{we\:know\:that}$

larger number exceeds four times the smaller one by 5.

बड़ी वाली संख्या, छोटी संख्या 5 से, चार गुना बड़ी संख्या है

$\bold{According\:to\:the\:question}$

$\implies{4(80-x) + 5 = x}$

$\sf{Solve\:the\:left\:hand\:side\:firstly...}$

$\implies{320 - 4x + 5 = x}$

$\implies{-4x - x= -325}$

$\sf{Solve\:the\:variables....}$

$\implies{-5x = -325}$

$\sf{Shift\:5\:to\:right\:hand\:side....}$

$\implies{x = \dfrac{325}{5}}$

$\sf{After\:cancelling....}$

$\implies{x = 65}$

$\sf{now,\:let\:find\:the\:numbers}$

$\therefore{\sf{Larger\:number = x = 65.}}$

$\therefore{\sf{Smaller\:number = 80-x= 80 - 65= 15.}}$

$\sf{So\:the\:final\:answer\:is\:-}$

$\boxed{\boxed{\sf{Smaller\:number = 15.}}}$