Time and W ork (MCQ)

1. A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Rs. 1500 for the whole work, the daily wages of B and C are:
1. Rs. 160
2. Rs. 225
3. Rs. 255
4. Rs. 350
5. Rs. 275

2. A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
1. 13 days
2. 16 days
3. 15 days
4. 22 days
5. 18 days

3. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days?
1. 15
2. 19
3. 23
4. data inadequate
5. None of these

4. Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they take to complete the remaining work?
1. 3 days
2. 5 days
3. 6 days
4. 9 days
5. None of these

5. 10 women can complete a work in  7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
1. 5 days
2. 8 days
3. 7 days
4. cannot be determined
5. None of these

6. Sixteen men can complete a work in twelve days. Twenty-four children can complete the same work in eighteen days. Twelve men and eight children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work?
1. 5 days
2. 4 days
3. 10 days
4. 9 days
5. None of these

7. Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days?
1. 18 men
2. 24 men
3. 36 men
4. 50 men
5. None of these

8. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacities of a woman and a boy are in the ratio:
1. 1 : 2
2. 2 : 1
3. 1 : 3
4. 6 : 7
5. 1 : 4

9. If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:
1. 2 : 1
2. 3 : 1
3. 3 : 2
4. 6 : 7
5. 1 : 4

Time and Work

Work
Work to be done is generally considered as one unit. It may be digging a trench constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.
General rules to be followed in the problems on Time and Work
1. If Acan do a piece of work in n days, then work done by Ain 1 day is 1/n. ie,if a person can do some work in 12 days, he does 1/ 12th of the work in one day.
2. If A s 1 day’s work = 1/n, then A can finish the whole work in n days. ie, if a person’s one day work is 1/10, then he can finish the whole work in 10 days.
3. If A is thrice as good a workman as B, then ratio of work done by A and B = 3 : 1. ie, if a man works three times as fast as a woman does, then when the work is complete, 3 parts of the work has been done by the man and 1 part by the woman.
4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1 : 3. ie, if the woman takes 15 days to complete the work, then the man takes 5 days to complete the same work.
5. If two persons A and B can individually do some work in a and b days respectively, then A and B together can complete the same work in ab (a + b) days.
6. The fundamental rules on variation also apply in Time and Work.
(i) Work and men are directly proportional to each other ie, if the work increases, the no. of men required to do it, also increases, if the work is to be completed in the same number of days.
(ii) Men and days are inversely proportional, ie, if the number of men increases, the number of days required to complete the same work decreases and vice versa.
(iii) Work and days are directly proportional, ie, if the work increases, the number of days required also increases, if the work is to be completed with the same number of men and vice versa.

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Unitary method(MCQ)

1. Cost of 24 pens is Rs. 96. Find the cost of 16 such pens.
(1) Rs. 66
(2) Rs. 64
(3) Rs. 62
(4) Rs. 68
(5) None of these

2. Cost of 8 dozen bananas is Rs. 180. How many bananas can be purchased for Rs. 30?
(1) 16 bananas
(2) 24 bananas
(3) 14 bananas
(4) 22 bananas
(5) None of these

3. A man pays Rs. 13000 as rent for 4 months. How much does he pay for the whole year, if rent per month remains the same?
(1) Rs. 48000
(2) Rs. 39000
(3) Rs. 46000
(4) Rs. 47000
(5) None of these

4. 23 envelopes cost Rs. 57.50. How many envelopes can be bought for Rs. 127.50.
(1) 55
(2) 56
(3) 51
(4) 53
(5) None of these

5. 20 men can reap a field in 20 days. When should 5 men leave the work, if the whole field is to be reaped in 24 days after they leave the work?
(1) 2 days
(2) 4 days
(3) 3 days
(4) 5 days
(5) None of these

Unitary method

Unitary Method

Direct Proportion

Two quantities are said to be directly proportional, if on the increase in one the other increases proportionally or on the decrease in one the other decreases proportionally.
eg, More the numbers of articles, more is the cost.
More the number of workers, more is the work done.
Less the number of articles, less is the cost.
Less the number of workers, less is the work done.

Indirect Proportion

Two quantities are said to be indirectly proportional, if on the increase in one the other decreases proportionally or on the decrease in one the other increases proportionally.
eg, More the number of workers, less is the number of days required to finish a work. More the speed, less is the time taken to cover a certain distance.
Less the number of workers, more is the number of days required to finish a work. Less the speed, more is the time taken to cover a certain distance.

Chain Rule

When a series of variables are connected with one another, that we know how much of the first kind is equivalent to a given quantity of second, how much of the second is equivalent to a given quantity of the third and so on. The rule by which we can find how much of the last kind is equivalent to a given quantity of the first kind is called the Chain Rule

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order of magnitude(MCQ)

1. Ramesh gave milk to have to his three sons Harish, Shayam and Ajay in three pots of the shape hemisphere, cube and cuboid. If radius of hemisphere pot is 5 cm, side of cubic pot is 5 cm and sides of cuboid pot are 5 cm × 5 cm × 6 cm, then who will get more milk?

(1) Harish
(2) Shayam
(3) Ajay
(4) Equal to all
(5) None of these

2. The velocity of sound in first medium is 320 m/s and in second medium is 1152 km/h. In which medium velocity of sound is maximum?
(1) First
(2) Second
(3) Equal in both
(4) Can’t be determined
(5) None of these

3. A minister of a village gave land to his four sons A, B, C and D. He gave them 5 hectare, 12 acre, 1600 sq m and 20 sq hectometre land respectively. Who got the maximum land?
(1) A
(2) B
(3) C
(4) D
(5) None of these

4. Aakash, Amar and Sawan has the lengths 20 decimetre, 1.7 m and 180 cm respectively. Who is the shortest?
(1) Aakash
(2) Amar
(3) Sawan
(4) All are of equal length
(5) None of these

5. Rotation period of four planets Mercury, Venus, Saturn and Earth are respectively 3784320 thousands, 4572720 thousand min, 166 yr and 365 days, 5 h, 56 min, 4 s. Which planet has the least rotation period?

(1) Mercury
(2) Venus
(3) Saturn
(4) Earth
(5) None of these

Oder of magnitude

Orders of Magnitude

Example 1: Ajay, Akshay and Saroj cover a distance of , 33500 m and 290 hactometre respectively in an hour. Who has the maximum speed?
Solution. Distance covered by Ajay = = 67 × 1000 m = 33500 m
Distance covered by Akshay = 33500 m
Distance covered by Saroj = 290 hactometre
= 290 × 100 m = 29000 m
Since, distance covered by Ajay and Akshay are maximum and equal. Hence, Ajay and Akshay have maximum speed.

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Partnership

When two or more than two persons run a business jointly, they are called partners in the business and the deal between them is known as partnership.

Partnership is of two types

1. Simple Partnership
2. Compound Partnership

1. Simple Partnership: When investments of all the partners are for the same period of time, the profit or loss is distributed among the partners in the ratio of their original investments.
Suppose A and B invest ` p and ` q respectively for a year in a business, then at the end of the year. Share of A’s profit (loss) : Share of B’s profit (loss) = p : q.
2. Compound Partnership: When investments of all the partners are for different period of time, then equivalent capitals are calculated for a unit of time and the profit or loss is divided in the ratio of the product of time and investment.
Suppose A and B invest ` p and ` q for x months and y months respectively, then Share of A’s profit (loss): Share of B’s profit (loss) = px : qy.

Partners are of two types

• (i) Working Partner, and
• (ii) Sleeping Partner

(i) Working Partner: A partner who manages the business is called a working partner.
(ii) Sleeping Partner: A partner who only invests the money is called a sleeping partner.

Suppose A and B invest ` p and ` q respectively for a year in a business, then at the end of the year. Share of A’s profit (loss) : Share of B’s profit (loss) = p : q.
2. Compound Partnership: When investments of all the partners are for different period of time, then equivalent capitals are calculated for a unit of time and the profit or loss is divided in the ratio of the product of time and investment.
Suppose A and B invest ` p and ` q for x months and y months respectively, then Share of A’s profit (loss): Share of B’s profit (loss) = px : qy.

Partners are of two types

• (i) Working Partner, and
• (ii) Sleeping Partner

(i) Working Partner: A partner who manages the business is called a working partner.
(ii) Sleeping Partner: A partner who only invests the money is called a sleeping partner.

Partnership MCQ

1. A and B entered into a partnership with investments of Rs. 15000 and Rs. 40000 respectively. After 3 months A left from the business. At the same time C joins with Rs. 30000. At the end of 9 months they got Rs. 7800 as profit. Find the share of B.
(1) Rs. 4800
(2) Rs. 600
(3) Rs. 2400
(4) Rs. 1200
(5) None of these

2. A started a business with Rs. 18000. After 4 months B joins with Rs. 24000. After 2 more months C joins with Rs. 30000. At the end of 10 months C received Rs. 1850 as his share. Find the total profit.
(1) Rs. 7955
(2) Rs. 7030
(3) Rs. 8510
(4) Rs. 6845
(5) None of these

3. Three partners started a business with Rs. 80000. At the end of the year they receive Rs. 1800, Rs. 3000 and Rs. 4800 as profit. Find the investment of the second person.
(1) Rs. 25000
(2) Rs. 40000
(3) Rs. 15000
(4) Rs. 32000
(5) None of these

4. A and B together invested Rs. 12000 in a business. At the end of the year, out of a total profit Rs. 1800 A’s share was Rs. 750. What was the investment of A?
(1) Rs. 5000
(2) Rs. 10000
(3) Rs. 12000
(4) Rs. 15000
(5) None of these

5. A started a business with a capital of Rs. 10000 and 4 months later, B joined him with a capital of Rs. 5000. What is the share of A in the total profit of Rs. 2000 at the end of the year?
(1) Rs. 800
(2) Rs. 1000
(3) Rs. 1500
(4) Rs. 1800
(5) None of these

6. A, B and C enter into a partnership. A contributes 320 for 4 months, B contributes Rs. 510 for 3 months, and C contributes Rs. 270 for 5 months. If the total profit is Rs. 208, find the profit share of the partner A.
(1) Rs. 76.50
(2) Rs. 64
(3) Rs. 67.50
(4) Rs. 46
(5) None of these