Compound Variation

Q.

One liter of sunflower oil is equal to how many kilograms?

Q.

What is Frequency and Bandwidth?

Q.

If 14 kg of pules cost Rs. 441, what is the cost of 22 kg of pulses :

(a) Rs. 627 (b) Rs. 649

(c) Rs. 671 (d) Rs. 693

Q.

If the list price of a book is reduced by $\mathrm{Rs}5$ a person can buy $5$ more books for $\mathrm{Rs}300$ Then the original cost of the book is?

Q.

John spent $\frac{3}{4}$ hours doing homework. If $\frac{1}{4}$ hours of that time was spent doing math homework, what fraction of his total time spent doing homework did he spend on math?

Q.

The diameter of a wheel is $1.26m.$ How far will it travel in $500$ revolutions$?$

Q.

Three workers can do a job in $28$ $\mathrm{hours}$. How many more workers are needed to do this job in $12$ $\mathrm{hours}$?

Q. The breadth of a rectangular garden is $\frac{2}{3}$ of its length. If its perimeter is $40\text{m}$, then find its length.

1. $10\text{m}$
2. $12\text{m}$
3. $8\text{m}$
4. $6\text{m}$

Q. 6 men working 9 hours a day can do a piece of work in 4 weeks. How many men are required working 8 hours a day for 3 weeks to complete the same work?

1. 9 men
2. 8 men
3. 12 men
4. 5 men

Q. Sneha plants 24 roses in a row, where each rose is 2 metre apart. What is the length of the row of roses from the begining to the end ?

Q.

Find the fourth proportional in $\frac{1}{3},\frac{2}{5},6$.

Q. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can the two of them complete the work together ?

1. 20 days
2. 25 days
3. 30 days
4. 35 days

Q.

Pretend you have a job building tricycles. If you had $100$ handle bars, $150$ wheels, and $75$ seats. How many pedals would you need in order to make $\$50.00$? Assume that every tricycle sells for$\$4.00$.

1. $21$

2. $26$

3. $30$

4. $42$

Q.

Question 60

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) The time taken by a train to cover a fixed distance and the speed of the train.
(ii) The disatnce travelled by CNG bus and the amount of CNG used.
(iii) The number of people working and the time to complete a given work.
(iv) Income tax and the income.
(v) Distance travelled by an auto-rickshaw and time taken.

Q. In three vessels the ratio of water and milk is 6 : 7, 5 : 9 and 8 : 7, respectively. If the mixtures of the three vessels are mixed together then what will be the ratio of water and milk?

1. 3691 : 4499
2. 15 : 13
3. 2498 : 3051
4. 7 : 19

Q.

In a sugar solution, $\frac{12}{25}$ - part is sugar. What percentage of solution is sugar?

Q. Two cogged wheels of which one has $32$ cogs and other $54$ cogs, work into each other. If the latter turns $80$ times in three quarters of a minute, how often does the other turn in $8$ seconds?

1. $48$
2. $135$
3. $24$
4. $36$

Q. The mess charges for $35$ students for $24$ days is Rs. $6300$. In how many days will the mess charges be Rs. $3375$ for $25$ students?

1. $18$ days
2. $15$ days
3. $12$ days
4. $9$ days

Q. $\text{Initial height of a plant is}50\text{cm. Each day}$
$\text{its height increases by}0.5\text{cm. Can the total}$
height of the plant be represented as a linear function of number of days? If yes, obtain the function.

1. No. It will not result in a linear function.
2. $\text{Yes. The function is}h=\frac{1}{2}d,$
   where, h is the height in cm, and d is the number of days.
3. $\text{Yes. The equation is}h=50+\frac{1}{2}d,$ where, h is the height in cm, and d is the number of days.
4. It is a relation but not a function.

Q.

An elevator says ‘Maximum weight $400$ kg’. If $4$ people weighing $94$ kg, $66$ kg, $40$ kg, and $75$ kg get in, how much more weight can the elevator still hold?

Q.

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of $200$ inches and a diameter of one-quarter of an inch has a resistance of $20$ ohms. Find the electrical resistance in a $500$ inch wire with the same diameter.

1. $50$ ohm
2. $60$ ohm
3. $55$ ohm
4. None of these

Q. $A,B$ and $C$ can do a job in $12,5$ and $20$ days respectively. How long will they take to complete the work together?

Q. If a car covers $82.5km$ in $5.5$ litres of petrol, how much distance will it cover in $13.2$ litres of petrol?

1. $120$
2. $198$
3. $200$
4. $150$

Q. If $120$ children consume $300$ liters of milk in $30$ days. In how many days will $30$ children consume $540$ liters of milk?

1. $144$
2. $216$
3. $169$
4. $343$

Q. Look at the given functions:


has the lesser rate of change.

1. Function A
2. Function B
3. Both
4. Can't be determined

Q.

A block of mass 250, 000 kg has a volume of 100 cm³. What is the density of the block?

1. $2500\frac{kg}{m^3}$

2. $2.5\frac{kg}{m^3}$

3. $250,000\frac{kg}{m^3}$

4. $25,000,000\frac{kg}{m^3}$

Q. If the total wages of $15$ labourers for $6$ days is $Rs8,000$, find the wages of $21$ labourers for $5$ days

Q. A train travelling at the rate of $37$ miles in $50$ minutes takes $6$ hours for a journey. How long will it take if it travels at the rate of $60$ miles in the $1\frac{1}{4}$ hours?

1. $5$ hours $33$ minutes
2. $6$ hours $33$ minutes
3. $6$ hours $30$ minutes
4. $5$ hours $30$ minutes

Q. Jackie has two solutions that are $2$ percent sulphuric acid and $12$ percent sulphuric acid by volume respectively. If these solutions are mixed in appropriate quantities to produce $60$ litres of a solution that is $5$ percent sulphuric acid, approximately how many litres of the $2$ percent solution will be required?

1. $24$
2. $36$
3. $20$
4. $42$
5. $18$

Q.

What do you mean by the statement, the density of mercury is 13.6 gm /cm³?