Question

A piece of string of 175 centimeters was cut into two pieces,the ratio of their lengths was 4:3. Find the length of smallest part.

Answer 1

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

• Length of string is 175 cm
• The given string which is 175 cm long is cut into two pieces in the ratio 4:3.

$\sf{\bold{\underline {Find}}}$

Length of the smallest string.

$\sf{\bold{\underline {Assume}}}$

Let the -

• smallest string be 3x cm.
• largest string be 4x cm.

$\sf{\bold{\underline {Solution}}}$

Largest string is 4x cm and smallest string is 3x cm and the total length of the whole string is 175 cm.

$\sf{\bold{\underline {According\:to\:question}}}$

⇒ 4x + 3x = 175

⇒ 7x = 175

⇒ x = 175/7

⇒ x = 25

So,

$\sf{\bold {Length \:of\:smallest\:string: }}$

⇒ 3(25)

⇒ 75 cm

$\sf{\bold {Length\:of\:latgest\:string:}}$

⇒ 4(25)

⇒ 100 cm

•°• Length of smallest string is 75 cm

Answer 2

$\huge \red { \boxed{ \boxed{ \mathsf{ \mid \ulcorner Answer : \urcorner \mid }}}}$

Given :-

Ratio :- 3 : 4

So,

Let the length of smallest string be 3a.

Let the length of largest string be 4a.

A. T. Q

4a + 3a = 175

7a = 175

a = 175/7

a = 25

_______________[Put values]

Hence,

The length if smallest string = 3a = 3(25) = 75 cm.

The length of largest string = 4a = 4(25) = 100 cm.

$\rule{200}{2}$

Verification :-

It is given that the length of the price of string is 175 cm.

So,

Add the length of both the larger and smaller string.

Hence,

100 + 75 = 175

175 = 175

LHS = RHS

Hence verified