Unitary Method

Q.

If $15$ workers can build a wall in $48hours$, how many workers will be required to do the same work in $30hours$? (Answer in numbers)

Q. A car can travel 30 km with 1 litre of petrol. Then, it will travel km with 5 litres of petrol.

1. 120
2. 150
3. 180

Q.

$A$ can do a piece of work in $14$ days which $B$ can do in $21$ days. They begin together but $3$ days before the completion of the work, $A$ leaves off. The total number of days to complete the work is:

1. $6\frac{3}{5}$

2. $8\frac{1}{2}$

3. $10\frac{1}{5}$

4. $13\frac{1}{2}$

Q. Question 116
If 16 shirts of equal size can be made out of 24 m of cloth, how much cloth is needed for making one shirt?

Q. A train is moving at a uniform speed of $75$ km/hour.
(i) How far will it travel in $20$ minutes?
(ii) Find the time required to cover a distance of $250$ km.
[4 marks]

Q.

Aakash bought vegetable weighing $10\text{kg}$. Out of this $3\text{kg 500 g}$ is onions , $2\text{kg 75 g}$ of tomatoes and the rest is potatoes .What is the weight of the potatoes ?

Q. A and B can independently finish a piece fo work in 36 and 45 days respectively. They started working together and after a few days A left. After that B could finish the remaining work in 36 days. After how many days of working together did A leave?

Q.

Which of the following are in inverse proportion?

1. The number of workers on a job and the time to complete the job.

2. The time is taken for a journey and the distance traveled at a uniform speed.

3. Area of cultivated land and the crop harvested.

4. The time is taken for a fixed journey and the speed of the vehicle.

5. The population of a country and the area of land per person.

Q. Question 05.
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?

Q.

A truck covers a distance of 510 km in 34 litres of diesel. How much distance would it cover in 20 litres of diesel ?

Q. A man takes 2 hours to cover a distance when he walks at 3 kilometres per hour (kmph). Find the time taken if he walks at the rate of 4 kmph.

Q.

The cost of 3 duck eggs is same as 4 hen eggs and the cost of 4 swan eggs is same as 7 duck eggs. Given that the cost of 2 hen eggs is ₹ 8, then find the cost of swan’s egg.

1. ₹ 8

2. ₹ 8.75

3. ₹ 9.33

4. ₹ 9

Q.

A man's salary was raised by 10% and then reduced by 10%.Find the percentage change in his salary

Q.

A and B together complete a piece of work in 15 days. They both started working together, but after 6 days B fell ill, so A took 30 more days to complete the work alone. How long will B take to complete the work alone?

1. 21 days

2. 20 days

3. 26 days

4. 23 days

Q. In how many ways can a president, a manager and a secretary be chosen from among $8$ candidates?

1. $343$
2. $336$
3. $8!$
4. $3!$

Q. Alfred buys an old scooter for Rs. $4700$ and spends Rs. $800$ on its repairs. If he sells the scooter for Rs. $5800$, his gain percent is:

1. $5\frac{5}{11}$%
2. $4\frac{4}{7}$%
3. $10$%
4. $12$%

Q. In a class there are $24$ boys whose ages is decreased by $4$ months, when new boy aged $20$ years is replaced by a new boy. Find the age of the new boy.

Q. If a boy walks from his house at $4$ km/hr he reaches school $10$ min early, if he walks at $3$ km/hr he reaches 10 min late. What is the distance from his house to school ?

1. $6$ km
2. $4.5$ km
3. $5$ km
4. $4$ km

Q.

Question 76(i)

An average Urban Indian uses about 150 L of water everyday.
$\begin{array}{cc}\text{Activity}& \text{Litres per person per day}\\ \text{Drinking}& 3\\ \text{Cooking}& 4\\ \text{Bathing}& 20\\ \text{Sanitation}& 40\\ \text{Washing clothes}& 40\\ \text{Washing utensils}& 20\\ \text{Gardening}& 23\\ \text{Total}& 150\end{array}$
What percent of water is used for bathing and sanitation together per day?

Q.

Question 03.
In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Q. A car can travel 30 km with 1 litre of petrol. Then, it will travel km with 5 litres of petrol.

1. 120
2. 150
3. 180

Q.

Question 06.
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?

Q. If 45 men and 60 boys can do a piece of work in 20 days. How many days will 15 men and 20 boys take to complete the work?

Q. A drum of kerosene oil is $\frac{3}{4}$ full. When $30$ litres of oil are drawn from it, it is $\frac{7}{12}$ full. Find the capacity of the drum ?

1. $140$ litres
2. $180$ litres
3. $240$ litres
4. $120$ litres

Q.

A factory requires 42 machines to produce a given number of articles in 63 days.
The number of machines required to produce the same number of articles in 54 days is 48.

1. 49

2. 36

Q. Question 10.1 .
Two persons could fit new windows in a house in 3 days.
One of the persons fell ill before the work started. How long would the job take now?

Q.

If the cost of 20 articles is ₹ 850, then cost of 35 articles is ₹ _____.

1. 15 days

2. 3 days

3. 12 days

4. 25 days

Q.

A book costs $₹m,$ pen costs $₹n$ more than half of the cost of book$.$ Express the total cost of a book and a pen in terms of $m$ and $n.$

Q. The following line graph shows the yearly sales figures for a manufacturing company.
(a) What were the sales in (i) $2002$ (ii) $2006$?
(b) What were the sales in (i) $2003$ (ii) $2005$?
(c) Compute the difference between the sales in $2002$ and $2006$.
(d) In which year was there the greatest difference between the sales as compared to its previous year?

Q. Find the square root of $5476$ by prime factorization.