Question

sonali worked as a salesgirl for 5 days working 5 3/4hours, 7 1/2hours, 6 1/6hours, 8 1/3hours, 7 1/4 hours each day . How much did she earn in 5 days at the rate of 25 3/4 per hour

Answer 1

Step-by-step explanation:

Area of triangle=

2

1

∣(x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

))∣ where x=1,x

2

=3,x

3

=5, y

1

=2,y

2

=7,y

3

=3

⇒

2

1

∣(1(7−3)+3(3−2)+5(2−7))∣

⇒

2

1

∣(1−(4)+3(1)+5(−5))∣

⇒

2

1

∣(4+3+(−25)∣

=

2

1

∣(−25+7)∣

=

2

1

∣(−18)∣

Area of triangle =9 cm

Answer 2

Given :

• Sonali worked as a salesgirl for 5 days working 5 3/4 hours, 7 1/2 hours, 6 1/6 hours, 8 1/3 hours, 7 1/4 hours each day.
• Rate  = Rs. 25 3/4 per hour

To find :

• how much did she earn in 5 days?

Solution :

⇒ Let's find how many hours did she work.

$\sf \longrightarrow 5 \dfrac{3}{4} = \dfrac{4 \times 5 + 3}{4} = \dfrac{20 + 3}{4} = \dfrac{23}{4} \: hours$

$\sf \longrightarrow 7 \dfrac{1}{2} = \dfrac{2 \times 7 + 1}{2} = \dfrac{14 + 1}{2} = \dfrac{15}{2} \: hours$

$\sf \longrightarrow 6 \dfrac{1}{6} = \dfrac{6 \times 6 + 1}{6} = \dfrac{36 + 1}{6} = \dfrac{37}{6} \: hours$

$\sf \longrightarrow 8 \dfrac{1}{3} = \dfrac{3 \times 8 + 1}{3} = \dfrac{24 + 1}{3} = \dfrac{25}{3} \: hours$

$\sf \longrightarrow 7 \dfrac{1}{4} = \dfrac{4 \times 7 + 1}{4} = \dfrac{28 + 1}{4} = \dfrac{29}{4} \: hours$

$\longrightarrow \sf \dfrac{23}{4} + \dfrac{15}{2} + \dfrac{37}{6} + \dfrac{25}{3} + \dfrac{29}{4}$

$\longrightarrow \sf \dfrac{23}{4} + \dfrac{15}{2} + \dfrac{29}{4} + \dfrac{37}{6} + \dfrac{25}{3}$

$\longrightarrow \sf \dfrac{23}{4} + \dfrac{29}{4} + \dfrac{15}{2} + \dfrac{37}{6} + \dfrac{25}{3}$

$\longrightarrow \sf \dfrac{23 + 29}{4} + \dfrac{15}{2} + \dfrac{37}{6} + \dfrac{25}{3}$

$\longrightarrow \sf \dfrac{52}{4} + \dfrac{15}{2} + \dfrac{37}{6} + \dfrac{25}{3}$

• LCM of 4, 2, 6 and 3 = 12

$\longrightarrow \sf \dfrac{52 \times 3 }{4 \times 3 } + \dfrac{15 \times 6}{2 \times 6} + \dfrac{37 \times 2 }{6 \times 2} + \dfrac{25 \times 4 }{3 \times 4}$

$\longrightarrow \sf \dfrac{156 }{12} + \dfrac{90}{12} + \dfrac{74 }{12} + \dfrac{100 }{12}$

$\longrightarrow \sf \dfrac{156 + 90 + 74 + 100 }{12}$

$\longrightarrow \sf \dfrac{420}{12}$

$\longrightarrow \sf \cancel{ \dfrac{420}{12} }$

$\longrightarrow \sf 35 \: hours$

$\tt \star Rate \: per \: hour = 25 \dfrac{3}{4} = \dfrac{4 \times 25 + 3}{4} = \dfrac{100+ 3}{4} = \dfrac{103}{4}$

$\tt \star Earned \: in \: 5 \: days = \dfrac{103}{4} \times 35$

$\tt \star Earned \: in \: 5 \: days = \dfrac{103}{4} \times \dfrac{35}{1}$

$\tt \star Earned \: in \: 5 \: days = \dfrac{103 \times 35}{4 \times 1}$

$\tt \star Earned \: in \: 5 \: days = \dfrac{3605}{4}$

$\tt \star Earned \: in \: 5 \: days = 901.25$

• Therefore, Sonali earned Rs. 3605/4 or Rs. 901.25 in 5 days.