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MATHS Case study (4 Marks)

Time and Work · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 2 questions.

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Case study (4 Marks)

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2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
Two labourers, Sohan and Mohan, were employed to dig a trench. Sohan alone can dig it in 10 days while Mohan alone can dig it in 15 days. In order to complete the job quickly both were hired together. They worked together, dug the trench and were paid ₹ 4000 altogether for the job. Mohan insisted that the money be divided equally between both of them as they had worked for the same time but Sohan said that he should get a bigger share, as the quantum of work done by him was greater.

(1) How many days did both of them together take to dig the trench?
(a) 5 days
(b) 6 days
(c) $7 \frac{1}{2}$ days
(d) 8 days
(2) What should be the fair share of Mohan and Sohan respectively in the total amount received for the job?
(a) ₹ 1500, ₹ 2500
(b) ₹ 2000, ₹ 2000
(c) ₹ 1600, ₹ 2400
(d) ₹ 1750, ₹ 2250
(3) What fraction of the trench was dug by Mohan?
(a) $\frac{1}{2}$
(b) $\frac{2}{3}$
(c) $\frac{1}{3}$
(d) $\frac{2}{5}$
(4) Had Sohan and Mohan worked on the job on alternate days, how much time would they have taken to dig the trench?
(a) 8 days
(b) 10 days
(c) 12 days
(d) 15 days
Answer
(1) (B) 6 days
Sohan's 1 day's work $=\frac{1}{10}$;
Mohan's 1 day's work $=\frac{1}{15}$.
(Sohan + Mohan)'s 1 day's work $=\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$.
Hence, Sohan and Mohan together do the work in 6 days.

(2) (C) ₹ 1600 , ₹ 2400
Ratio of shares of Mohan and Sohan = ratio of their 1 day's work
$=\frac{1}{15}: \frac{1}{10}=2: 3$.
So, Mohan's share $=₹\left(4000 \times \frac{2}{5}\right)=₹ 1600 ;$
Sohan's share $=₹\left(4000 \times \frac{3}{5}\right)=₹ 2400$.

(3) (D) $\frac{2}{5}$
Required fraction $=$ Mohan's 6 day's work $=\left(\frac{1}{15} \times 6\right)=\frac{2}{5}$.

(4) (C) 12 days
(Sohan + Mohan)'s 2 day's work $=\left(\frac{1}{10}+\frac{1}{15}\right)=\frac{3+2}{30}$
$=\frac{5}{30}=\frac{1}{6}$.
$\therefore $ total time taken $=(2 \times 6)$ days $=12$ days.
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Question 24 Marks
Two labourers, Sohan and Mohan, were employed to dig a trench. Sohan alone can dig it in 10 days while Mohan alone can dig it in 15 days. In order to complete the job quickly both were hired together. They worked together, dug the trench and were paid 4000 altogether for the Job. Mohan insisted that the money be divided equally between both of them as they had worked for the same time but Sohan said that he should get a bigger share, as the quantum of work done by him was greater.

(1) How many days did both of them together take to dig the trench?
(a) 5 days (b) 6 days (c) $7 \frac{1}{2}$ days (d) 8 days

(2) What should be the fair share of Mohan and Sohan respectively in the total amount received for the job?
(a) ₹1500, ₹2500 (b) ₹2000, ₹2000 (c) ₹1600, ₹2400 (d) ₹1750, ₹2250

(3) What fraction of the trench was dug by Mohan?
(a) $\frac{1}{2}$ (b) $\frac{2}{3}$ (c) $\frac{1}{3}$ (d) $\frac{2}{5}$

(4) Had Sohan and Mohan worked on the job on alternate days,how much time would they have taken to dig the trench?
(a) 8 days (b) 10 days (c) 12 days (d) 15 days
Answer
self
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Case study (4 Marks) - MATHS STD 8 Questions - Vidyadip