## Selina Concise Mathematics class 7 ICSE Solutions – Unitary Method (Including Time and Work)

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The method in which the value of a unit (one) quantity is first calculated to get the value of any other quantity is called the unitary method.

In unitary method, we come across two types of variations :

(i) Direct-variation

(ii) Inverse-variation.

**(i) Direct variation :** Increase in one quantity causes increase in the other and decrease in one quantity causes decrease in the other.

**(ii) Inverse variation :** Increase in one quantity causes decrease in the other and decrease in one quantity causes increase in the other.

This is found in the sums of speed, work done etc.

**EXERCISE 7 (A)**

**Question 1.**

**Weight of 8 identical articles is 4.8 kg. What is the weight of 11 such articles ?**

**Answer:**

Weight of 8 articles = 4.8 kg

Weight of 1 article = \(\frac { 4.8 }{ 8 }\) kg

and weight of 11 articles =\(\frac { 4.8 }{ 8 }\) x 11 kg

= 0.6 x 11 = 6.6 kg

**Question 2.**

**6 books weigh 1 .260 kg. How many books will weigh 3.150 kg ?**

**Answer:**

**Question 3.**

**8 men complete a work in 6 hours. In how many hours will 12 men complete the same work ?**

**Answer:**

8 men can complete a work in = 6 hours

1 man can complete the work in = 6×8 hours

12 men can complete the work in = \(\frac { 6 x 8 }{ 12 }\) = 4 hours

**Question 4.**

**If a 25 cm long candle burns for 45 minutes, how long will another candle of the same material and same thickness but 5 cm longer than the previous one, burn ?**

**Answer:**

25 cm long candle burn in = 45 minutes

1 cm long candle will burn in = \(\frac { 45 }{ 25 }\) mintues

25 + 5 = 30 cm long candle will burn in

= \(\frac { 45 x 30 }{ 25 }\)minutes = 54 minutes

**Question 5.**

**A typist takes 80 minutes to type 24 pages. How long will he take to type 87 pages ?**

**Answer:**

For typing 24 pages, time is required = 80 minutes

For typing 1 page, time is required =\(\frac { 80 }{ 24 }\) minutes

and for typing 87 pages, time is required

= \(\frac { 80 x 87 }{ 24 }\) minutes = 290 minutes

**Question 6.**

**Rs. 750 support a family for 15 days. For how many days will Rs. 2,500 support the same family ?**

**Answer:**

Rs. 750, can support a family for = 15 days

Re. 1 will support for = \(\frac { 15 }{ 750 }\)days

and Rs. 2,500 will support for = \(\frac { 15 }{ 750 }\)x 2500 days = 50 days

**Question 7.**

**400 men have provisions for 23 weeks. They are joined by 60 men. How long will the provisions last ?**

**Answer:**

400 men have provisions for = 23 weeks

1 man will have provisions for = 23 x 400 weeks

and 400 + 60 = 460 men will have provisions for = \(\frac { 23 x 400 }{ 460 }\) weeks = 20weeks

**Question 8.**

**200 men have provisions for 30 days. If 50 men left, the same provisions would last for the remaining men, in how many days?**

**Answer:**

200 men have provisions for = 30 days

1 man will have provisions for = 30 x 200 days

200 – 50 = 150 men will have provisions

for = \(\frac { 30 x 200 }{ 150 }\) days = 40 days

**Question 9.**

**8 men can finish a certain amount of provisions in 40 days. If 2 more men join with them, find for how many days the same amount of provisions be sufficient ?**

**Answer:**

8 men can finish a provision in = 40 days

1 man will finish in = 40 x 8 days

8+2=10 men will finish in =\(\frac { 40 x8 }{ 10 }\)

= 32 days

**Question 10.**

**If interest on Rs. 200 be Rs. 25 in a certain time, what will be the interest on Rs 750 for the same time ?**

**Answer:**

**Question 11.**

**If 3 dozen eggs cost Rs. 90, find the cost of 3 scores of eggs. (1 score = 20)**

**Answer:**

3 dozen = 3 x 12 = 36 eggs,

3 scores = 3 x 20 = 60

The cost of 36 eggs is = Rs. 90

The cost of 1 egg will be = Rs. \(\frac { 90 }{ 36 }\)

∴ Cost of 60 eggs will be = Rs. \(\frac { 90 x60 }{ 36 }\)

= Rs. 150

**Question 12.**

**If the fare for 48 km is Rs. 288, what will be the fare for 36 km ?**

**Answer:**

Fare for 48 km = Rs. 288

fare for 1 km = Rs. \(\frac { 288 x 36 }{ 48 }\) = Rs. 216

**Question 13.**

**What will be the cost of 3.20 kg of an item, if 3 kg of it costs Rs. 360 ?**

**Answer:**

**Question 14.**

**If 9 lines of a print, in a column of a book contains 36 words. How many words will a column of 51 lines cqntain ?**

**Answer:**

**Question 15.**

**125 pupil have food sufficient for 18 days. If 25 more pupil join them, how long will the food last now ? What assumption have you made to come to your answer ?**

**Answer:**

Pupils in the beginning = 125

More pupils joined = 25

Total pupils = 125 + 25 = 150

Food is sufficient for 125 pupils for = 18 days

Food will be sufficient for 1 pupil for = 18 x 125 days (less pupil more days)

and food will be sufficient for 150 pupils = \(\frac { 18 x 125 }{ 150 }\) days (more pupil more days)

= \(\frac { 18 x 5 }{ 6 }\) 15 days

**Question 16.**

**A carpenter prepares a new chair in 3 days, working 8 hours a day. Atleast how many hours per day must he work in order to make the same chair in 4 days ?**

**Answer:**

A chair is completed in 3 days working per day = 8 hours

Then their will be completed in 1 day working for = 8 x 3 hours per day (less days more hours)

and it will be completed in 4 days working for = \(\frac { 8 x 3 }{ 4 }\)= 6 hours per day.

**Question 17.**

**A man earns ₹5,800 in 10 days. How much will he earn in the month of February of a leap year?**

**Answer:**

**Question 18.**

**A machine is used for making rubber balls and makes 500 balls in 30 minutes. How many balls will it make in 3\(\frac { 1 }{ 2 }\) hours?**

**Answer:**

**Question 19.**

**In a school’s hostel mess, 20 children consume a certain quantity of ration in 6 days. However, 5 children did not return to the hostel after holidays. How long will the same amount of ration last now?**

**Answer:**

Total number of children = 20

20 children consume a certain quantity of ration in = 6 days

1 children consume a certain quantity of ration in = 6 x 20 days

As 5 children did not return to the hostel after holidays.

Then number of children in hostel = 20-5 = 15

Hence, 15 children consume certain quantity 6×20

of ration in = \(\frac { 6 x 20 }{ 15 }\) days = 8 days

**EXERCISE 7 (B)**

**Question 1.**

**Answer:**

**Question 2.**

**3\(\frac { 1 }{ 2 }\)m of cloth costs Rs. 168 ; find the cost of 4\(\frac { 1 }{ 3 }\)m of the same cloth.**

**Answer:**

**Question 3.**

**A wrist watch loses 10 sec in every 8 hours; in how much time will it lose 15 sec. ?**

**Answer:**

**Question 4.**

**In 2 days and 20 hours, a watch gains 20 sec ; find how much time will the watch take to gain 35 sec. ?**

**Answer:**

**Question 5.**

**50 men mow 32 hectares of land in 3 days. How many days will 15 men take to mow it?**

**Answer:**

Land is same in both the cases.

Now 50 men can mow land in = 3 days

∴ 1 man will mow it in = 3 x 50 days

and 15 men will mow it in = \(\frac { 3 x 50 }{ 15 }\) = 10 days

**Question 6.**

**The wages of 10 workers for a six days week are Rs, 1,200. What are the one day wages: (i) of one worker ? (ii) of 4 workers?**

**Answer:**

**Question 7.**

**If 32 apples weigh 2 kg 800 g. How many apples will there be in a box, containing 35 kg of apples ?**

**Answer:**

**Question 8.**

**A truck uses 20 litres of diesel for 240 km. How many litres will be needed for 1200 km?**

**Answer:**

For 240 km, diesel is needed = 20 litres

∴ for 1 km, diesel will be needed 20

**Question 9.**

**A garrison of 1200 men has provisions for 15 days. How long will the provisions last if the garrison be increased by 600 men ?**

**Answer:**

1200 men has provision for = 15 days

1 man will have that provision for = 15 x 1200 days

∴1200 + 600 = 1800 men will has that provisions for =\(\frac { 15 x 1200 }{ 1800 }\)days

= 10 days

**Question 10.**

**A camp has provisions for 60 pupil for 18 days. In how many days, the same provisions will finish off if the strength of the camp is increased to 72 pupil ?**

**Answer:**

60 pupil have provision for = 18 days 1 pupil will have provision for = 18 x 60 days (less pupils more days)

and 72 pupils will have provision for = \(\frac { 18 x 60 }{ 72 }\) days

= 15 days.

**EXERCISE 7 (C)**

**Question 1.**

**A can do a piece of work in 6 days and B can do it in 8 days. How long will they take to complete it together ?**

**Answer:**

**Question 2.**

**A and B working together can do a piece of work in 10 days B alone can do the same work in 15 days. How long will A alone take to do the same work ?**

**Answer:**

**Question 3.**

**A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in : (i) one day (ii) 2 days.**

** What part of work will be left, after they have worked together for 2 days ?**

**Answer:**

**Question 4.**

**A and B take 6 hours and 9 hours respectively to complete a work. A works for 1 hour and then B works for two hours.**

** (i) How much work is done in these 3 hours ?**

** (ii) How much work is still left ?**

**Answer:**

**Question 5.**

**A, B and C can do a piece of work in 12, 15 and 20 days respectively. How long will they take to do it working together ?**

**Answer:**

**Question 6.**

**Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together ?**

**Answer:**

**Question 7.**

**Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days.**

** Find:**

** (i) work done by Mohit in 20 days.**

** (ii) work left after Mohit has worked on it for 20 days.**

** (iii) time taken by Anuj to complete the remaining work.**

**Answer:**

**Question 8.**

**Joseph and Peter can complete a work in 20 hours and 25 hours respectively.**

** Find : (i) work done by both together in 4 hrs.**

**(ii) work left after both worked together for 4 hrs.**

**(iii) time taken by Peter to complete the remaining work.**

**Answer:**

**Question 9.**

**A is able to complete \(\frac { 1 }{ 3 }\) of a certain work in 10 hrs and B is able to complete\(\frac { 2 }{ 5 }\) of the same work in 12 hrs.**

** Find:**

** (i) how much work can A do in 1 hour ?**

** (ii) how much work can B do in 1 hour ?**

** (iii) in how much time will the work be completed, if both work together.**

**Answer:**

**Question 10.**

**Shaheed can prepare one wooden chair in 3 days and Shaif can prepare the same chair in 4 days. If they work together, in how many days will they prepare :**

** (i) one chair ? (ii)14 chairs of the same kind?**

**Answer:**

**Question 11.**

**A, B and C together finish a work in 4 days. If A alone can finish the same work in 8 days and B in 12 days, find how long will C take to finish the work.**

**Answer:**