Question

A can do a piece of work in 10 days; b in 15 days. They work for 5 days. The rest of the work was finished by c in 2 days. If they get 1500 for the whole work, the daily wages of b and c are

Answer 1

Given :

• A can do a piece of work in 10 days
• B can do in 15 days
• A and B works for 5 days.
• Remaining work was done by C in 2 days
• Wages of A, B and C → ₹ 1500

To Find :

• Daily wages of B and C.

Solution :

Time taken by A → 10 days.

•°• A can complete →1/10 part of work in one day.

Time taken by B → 15 days.

•°• B can complete → 1/15 part of work in one day.

Work done in 5 days :

Work done by A :

• $\mathtt{\dfrac{5}{10}}$

• $\mathtt{\dfrac{1}{2}}$

Work done by B :

• $\mathtt{\dfrac{5}{15}}$

• $\mathtt{\dfrac{1}{3}}$

Given that, C does the remaining work in 2 days.

Remaining work :

➤ $\mathtt{1\:-\:\Big({\dfrac{1}{2}\:+\:{\dfrac{1}{3}\Big)}}}$

➤ $\mathtt{1-\Big({\dfrac{3+2}{6}\Big)}}$

➤ $\mathtt{1-{\dfrac{5}{6}}}$

➤ $\mathtt{\dfrac{6-5}{6}}$

➤ $\mathtt{\dfrac{1}{6}}$

Total wages → ₹ 1500

A's share :

• $\mathtt{\dfrac{1}{2}\:\times\:1500}$

• $\mathtt{\dfrac{1500}{2}}$

• $\mathtt{750}$

$\large{\boxed{\mathtt{\purple{A's\:wage\:for\:5\:days\:=\:Rs.\:750}}}}$

B's share :

• $\mathtt{\dfrac{1}{3}\:\times\:1500}$

• $\mathtt{\dfrac{1500}{3}}$

• $\mathtt{500}$

$\large{\boxed{\mathtt{\red{B's\:wage\:for\:5\:days\:=\:Rs.\:500}}}}$

C's share :

• $\mathtt{\dfrac{1}{6}\:\times\:1500}$

• $\mathtt{\dfrac{1500}{6}}$

• $\mathtt{250}$

$\large{\boxed{\mathtt{\purple{C's\:wage\:for\:2\:days\:=\:Rs.\:250}}}}$

Share in daily wages :

★ B worked for 5 days.

•°• One day salary of B will be the result obtained after dividing B's wage for 5 days i.e ₹ 500 by 5.

• $\mathtt{\dfrac{500}{5}}$

• $\mathtt{100}$

•°• B's daily wage → ₹ 100.

C's daily wage :

★ C worked for 2 days.

•°• One day salary of C will be the result obtained after dividing C's wage for 2 days i.e ₹ 250 by 2.

• $\mathtt{\dfrac{250}{2}}$

• $\mathtt{125}$

•°• C's daily wage → ₹ 125.

Daily wages of B And C :

★ The daily wage of B and C will be sum of daily wage of B and C.

• $\mathtt{100+125}$

• $\mathtt{225}$

$\large{\boxed{\tt{\red{Daily\:wages\:of\:B\:and\:C\:=\:Rs.\:225}}}}$

Answer 2

$\huge\bold\green{Question}$

A can do a piece of work in 10 days; b in 15 days. They work for 5 days. The rest of the work was finished by c in 2 days. If they get 1500 for the whole work, the daily wages of b and c are ____

$\huge\bold\green{Answer}$

According to the question we have given :-

°•° A can do work in = 10 days

°•° B can do in = 15 days

°•° A and B both works for = 5 days

°•° Remaining work was done by C in 2 days

°•° Total Wages of A , B and C → ₹ 1500

So, we have to find :-

Daily wages of B and C

So , let's start

•→ Total Time taken by “ A ” → 10 days.

A can complete →1/10 part of work in a day

•→ Time taken by “ B ” → 15 days

B can complete → 1/15 part of work in a day

Hence , Work done in 5 days are :-

Work done by A :-

$\implies\sf{\cancel\dfrac{5}{10}}$

$\implies\sf{\dfrac{1}{2}}$

Work done by B :-

$\implies\sf{\cancel\dfrac{5}{15}}$

$\implies\sf{\dfrac{1}{3}}$

So, according to the question it is given that C does the remaining work in 2 days.

Remaining work :-

$\implies\sf{1\:-\:{\dfrac{1}{2}\:+\:{\dfrac{1}{3}}}}$

$\implies\sf{1-\Big({\dfrac{3+2}{6}}}$

$\implies\sf{\dfrac{6-5}{6}}$

$\implies\sf{\dfrac{1}{6}}$

Hence , Total wages are → ₹ 1500

So, share by A are :-

$\implies\sf{\dfrac{1}{2}\:\times\:1500}$

$\implies\sf{\dfrac{1500}{2}}$

Hence , total wage of A for 5 days = Rs.750

So, share by B are :-

$\implies\sf{\dfrac{1}{3}\:\times\:1500}$

$\implies\sf{\cancel\dfrac{1500}{3}}$

Hence , total wage of B for 5 days = Rs. 500

So, share by C are :-

$\implies\sf {\dfrac{1}{6}\:\times\:1500}$

$\implies\sf{\cancel\dfrac{1500}{6}}$

Hence , total wage of C for 2 days = Rs. 250

Share in daily wages :

Hence , B worked for 5 days then

•→ One day salary of B will be the result obtained after dividing B's wage for 5 days i.e ₹ 500 by 5.

= So, B's daily wage → ₹ 100.

C's daily wage are :-

Hence , C worked for 2 days.

•→ One day salary of C will be the result obtained after dividing C's wage for 2 days [ ₹ 250 by 2 ]

= So, C's daily wage → ₹ 125.

Daily wages of B And C :

The daily wage of B and C will be sum of daily wage of B and C.

So , daily wages of B and C is

= 100 + 125

= 225

Hence the Daily wages of B and C

are ruppes 225