Time and Work (समय र काम)-Numerical Reasoning Test

Basic Concept

• Ram can make 1 chair in 2 days => Ram can make 7 chair in 14 days; (रामले २ दिनमा १ कुर्सी बनाउन सक्छ => रामले १४ दिनमा ७ कुर्सी बनाउन सक्छ)

• Shyam can make 1 chair in 1 day=> Ram can make 7 chairs in 7 days; (रामले 1 दिनमा 1 कुर्सी बनाउन सक्छ => रामले 7 दिनमा 7 कुर्सी बनाउन सक्छ)

Therefore, Time↑ Work↓

i.e. If A can do a piece of work in x days than in 1 day A can do 1/x work. (यदि A ले एउटा काम गर्न x दिन लगाउछ भने; 1 दिन मा 1/x )

If someone does work faster(have more effeciency) then the work will be completed in less time (यदि कसैले छिटो काम गरेमा (अधिक दक्षता) कम समयमा काम पूरा हुनेछ)

Example: If you run faster then you can reach to your destination in shorter span of time. (यदि तपाईं छिटो दौडनुभयो भने, तपाईं छोटो समयमा आफ्नो गन्तव्यमा पुग्न सक्नुहुन्छ।)

Restricted

Please avoid relying on the old mindset of solving problems using the unitary method or the work-done relation method. You will have only 30 minutes to complete 60 questions, allowing an average of 30 seconds per question. At most, you can allocate up to 1 minute for some questions assuming that you complete some questions within 10-15 seconds. Based on past trends, the questions are generally very simple and can be completed quickly if approached logically.

(कृपया एकात्मक विधि वा कार्य-सम्पन्न सम्बन्ध विधि प्रयोग गरेर समस्याहरू समाधान गर्ने पुरानो मानसिकतामा भर नपर्नुहोस्। तपाईंसँग ६० प्रश्नहरू पूरा गर्न केवल ३० मिनेट मात्र हुनेछ, प्रति प्रश्न औसत ३० सेकेन्डको अनुमति दिँदै। तपाईले केहि प्रश्नहरूको लागि 1 मिनेट सम्म छुट्याउन सक्नुहुन्छ कि तपाईले 10-15 सेकेन्ड भित्र केहि प्रश्नहरू पूरा गर्नुभयो। विगतका प्रचलनहरूमा आधारित, प्रश्नहरू सामान्यतया धेरै सरल हुन्छन् र तार्किक रूपमा सम्पर्क गर्दा छिट्टै पूरा गर्न सकिन्छ)

Where,

P= no of persons

H= No of Hours

D= Days

W= Work

Formula 1 applies in cases where all variables—persons, hours, days, and work—are provided. The formula can also be expressed without the hours variable or without the work variable (assuming 𝑊=1 ), leading to the existence of Formula 2. (सूत्र 1 सबै चरहरू-व्यक्ति, घण्टा, दिन, र काम प्रदान गरिएका अवस्थामा लागू हुन्छ। सूत्रलाई घण्टा चर बिना वा कार्य चर बिना (𝑊=1 मान्दै) व्यक्त गर्न सकिन्छ, जसले सूत्र 2 को अस्तित्वमा पुर्‍याउँछ।)

• more men can do work in shorter period of time (धेरै पुरुषहरूले छोटो समयमा काम गर्न सक्छन्)
• if people spend more hours per day then work is completed in shorter days and vice versa(यदि मानिसहरूले दिनमा धेरै घण्टा खर्च गर्छन् भने काम छोटो दिनमा पूरा हुन्छ र यसको विपरीत)

Type 1: If 72 mens can build a wall of 280m in 21 days, how many men could take 18 days to build a similar type of wall of length 100 m ?

Here,

P1= 72; D1= 21; W1= 280

P2= ?; D2= 18; W2= 100

(P1D1) / (P2D2) = W1 / W2

72 * 21 / P2 * 18 = 280 / 100

=> P2= 30

Type 2: 39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work?

Here

P1 * H1 * D1 = P2 * H2 * D2

39 * 5 * 12 = 30 * H2 * 6

H2= 13

Type 3: 15 men can type 3240 pages in 6 days working 2 hours per day. How many men would be required to type 5400 pages working 4 hours per day for 3 days?

(15 * 2 * 6)/ (P2 * 4 * 3) = 3420/ 5400 [Formula 1]

P2= 25

Type 4: If four mens and 5 womens can do a work in 25 days then in how many days can 20 men and 25 women complete the work together?

4 M+ 5 W=>25 days.......... (i)

20 M+25 W=>?............... (ii)

or, 5(4 M + 5 W)=> 25/5

Since Work and days are inverse in relation we can directly say that the multiple of increment in workers leads to divisible of the same number of days.(काम र दिनहरू सम्बन्धमा उल्टो भएकाले हामी सिधै भन्न सक्छौं कि कामदारहरूको वृद्धिको गुणनले दिनहरूको समान संख्यालाई भाग गर्छ।)

More people take less days and viceversa by the same ratio of people.

Type 5: 6 Men and 8 boys can do a piece of work in 10 days where, 26 Men and 48 boys can do it in 2 days. In how many days 15 men and 20 boys complete the same work.

a. 3 days

b. 4 days

c. 5 days

d. 6 days

Explanation

6 M + 8 B => 10 days

15 M + 20 B =? (10/2.5) = 100/25= 4days [ Since, 6*2+6/2=15 and 8*2+8/2=20 (i.e. * 2.5 )and Work and Days are inverse in relation]

Type 6: A can do a chair in 10 days. B can same chair in 15 days. In how many days can both complete the same work together?

a. 5 days

b. 6 days

c. 8 days

d. 10 days

Type 7: If A and B can do a piece of work in 15 days, B alone can do the same work in 20 days; Then find in how many days A alone can complete the whole work.

a. 60 days

b. 45 days

c. 40 days

d. 30 days

Note: These concepts are sufficient for Nepali army officer cadet questions with respect to give time constraints. (यी अवधारणाहरू नेपाली सेनाका अधिकृत क्याडेटका प्रश्नहरूको लागि समय बाधा दिने सन्दर्भमा पर्याप्त छन्।)