Problem Based on Unitary Method

**Category : **4th Class

**If Jack types 75 words in 1 minute. How much time will he take to type 33750 words?**

**Solution:**

\[\because\] Jack types 75 words in 1 minute.

\[\therefore\] He will type 33750 words in \[\frac{33750}{75}\] minutes.

Thus, Jack will take 450 minutes to type 33750 words.

**If 15 computers costs Rs. 29250, find the cost of 12 computers.**

**Solution:**

Cost of 15computers = Rs. 29250

Cost of 1 computer = Rs. \[\frac{29250}{15}\] = Rs. 1950

Therefore, cost of 12 computers = Rs. \[\text{195}0\times \text{12}\] = Rs. 23400

**A train is running at a uniform speed. It covers 324567 km in 27 hours and reaches from A to B. How long will it take to go from station B to C, if distance between B to C is 72126km? **

**Solution:**

The distance covered by the train in 27 hours = 324567 km.

The distance covered by the train in 1 hour \[=\frac{324567}{27}km\]

=12021 km

\[\because\] The train takes 1 hour to cover the distance 12021 km.

\[\therefore\] Time taken by the train to cover the distance 72126 km

\[=\frac{72126}{12021}\] hour = 6 hours.

**If 4 workers can complete a work in 20 days, in how many days same work will be completed if 20 workers are employed?**

**Solution:**

\[\because\] 4 workers can complete the work in 20 days.

\[\therefore\] 1 worker can complete the work in \[4\times 20\] days.

\[\therefore\] 20 workers can complete the job in \[\frac{4\times 20}{20}\] days. Thus 20 workers can complete the job in 4 days.

To get more value we multiply.

To get less value we divide.

Value of units is found.

The value of the required unit is found.

The unitary method is a technique in elementary algebra for solving a class of problems in variation.

Unitary method consists of altering one of the variables to a single unit, i.e. 1, and then performing the operation necessary to alter it to the desired value.

**A factory produces 625149 dolls in 27 days. How many dolls can it produce in 18 days?**

(a) 416788

(b) 516766

(c) 416966

(d) 416766

(e) None of these

**Answer (d)**

**Explanation-**

Number of dolls produced by the factory in 27 days = 625149.

Number of dolls produced by the factory in 1 day = \[=\frac{625149}{27}\] .

Number of dolls produced by the factory in 18 days = \[=\frac{625149}{27}\times 18=416766\]

**Arwin earns Rs. 5404 in a week. How much money does he earn in 17 days?**

(a) Rs. 3124

(b) Rs.13127

(c) Rs. 3184

(d) Rs. 10124

(e) None of these

**Answer (a)**

**Explanation-**

Arwin earns Rs. 5404 in 7 days. His earning in 1 day

\[=\frac{5404}{7}\] His earning in 17 day

\[=\frac{5404}{7}\times 17=\] Rs.13124

**If 784530 balls can be put in 5 boxes, how many boxes are required to put 2824308 balls?**

(a) 12

(b) 13

(c) 18

(d) 20

(e) None of these

** Answer (c)**

**There are 4160 chairs in a hall. If each of the chairs cost Rs. 125, find the cost of all chairs altogether.**

(a) Rs. 520000

(b) Rs. 500000

(c) Rs. 525000

(d) Rs. 550000

(e) None of these

**Answer (a)**

**A car covers the distance of 1350 km in 18 hours. Find the distance covered by the car in 24 hours.**

(a) 1400km

(b) 1800km

(c) 1600km

(d) 2000km

(e) None of these

**Answer (b)**

**There are 152 students in a class. Each of the students contributed Rs. 40 for planting trees around the school. If planting one tree costs Rs. 20, how many trees can be planted by the money collected from the students? **

(a) 208

(b) 308

(c) 304

(d) 405

(e) None of these

**Answer: (b)**

**If 16 liters of petrol is consumed by a car in covering a distance of 4864 km, how many kilometers will it go in 32 liters of petrol?**

(a) 9728km

(b) 9600km

(c) 7280km

(d) 9715km

(e) None of these

**Answer: (a)**

**If 15 books cost Rs. 2540. find the cost of 24 books.**

(a) Rs.4564

(b) Rs. 4064

(c) Rs. 4625

(d) Rs. 4060

(e) None of these

**Answer: (b)**

*play_arrow*Introduction*play_arrow*Problem Based on Unitary Method*play_arrow*Unitary Method*play_arrow*Unitary Method

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