Sample QuestionsUnitary Method questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark against the correct answer in the following: A tree $6m$ tall casts a $4m$ long shadow. At the same time a flag pole casts a $50m$ long shadow. How long is the flag pole$?$
- A
$50m$
- ✓
$75m$
- C
$33\frac{1}{3}\text{m}$
- D
Answer: B.
View full solution →Mark against the correct answer in the following:
A garrison of $500$ men had provisions for $27$ days. After $3$ days, a reinforcement of $300$ men arrived. The remaining food will now last for how many days$?$
Answer: A.
View full solution →Mark against the correct answer in the following: If $4.5\ m$ of a uniform rod weighs $17.1\ kg,$ what is the weight of $12\ m$ of such a rod$?$
- A
$51.2\ kg$
- B
$53\ kg$
- ✓
$45.6\ kg$
- D
$56\ kg$
Answer: C.
View full solution →Mark against the correct answer in the following: $6$ dozen eggs are bought for $Rs.108.$ How much will $108$ eggs cost$?$
- A
$Rs. 171$
- ✓
$Rs. 162$
- C
$Rs. 153$
- D
$Rs. 180$
Answer: B.
View full solution →Mark against the correct answer in the following: In a race, Raghu covers $5\ km$ in $20$ minutes, how much distance will he cover in $50$ minutes $?$
- A
$10.5\ km$
- B
$12\ km$
- ✓
$12.5\ km$
- D
$13.5\ km$
Answer: C.
View full solution →Assertion (A): Speed varies inversely as the time taken to cover a certain distance.
Reason (R): More the speed, more is the distance covered in a certain time.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: B.
View full solution →Assertion (A): If 25 men can complete a work in 42 days then 30 men can complete the same work in 35 days.
Reason (R): More men at work, more is the work done.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: B.
View full solution →Assertion (A): The work done varies inversely as the number of men at work.
Reason (R): Less men at work, lesser is the work done.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): If 5 pens cost ₹ 60 then 15 pens will cost $₹ 180$.
Reason (R): The cost of articles varies directly as the number of articles.
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Write $'T'$ for true and $'F'$ for false for the following: If $8$ men can finish a piece of work in $40$ days then $10$ men can finish it in $32$ days.
View full solution →Mark against the correct answer in the following: If $12$ workers finish a piece of work in $4$ hours, then $15$ workers will finish it in _____ hrs _____ min.
View full solution →Write $'T'$ for true and $'F'$ for false for the following: tree $6m$ tall casts a shadow of length $4m$. At the same time a flag casts a shadow of length 50m. The length of the pole is $75m$.
View full solution →Fill in the blank: If $42$ men can dig a trench in $14$ days, then $1$ man can dig it in _____ days.
View full solution →Mark against the correct answer in the following: If $15$ oranges cost $Rs\ 60$, then $12$ oranges cost Rs _____.
View full solution →A car can cover $270\ km$ in $15$ litres of petrol. How many kilometres will it cover in $8$ litres of petrol$?$
View full solution →A bus covers a certain distance in $3$ hours $20$ minutes at an average speed of $45\ km$ per hour. How much time will it take to cover the same distance at a speed of $50\ km$ per hour$?$
View full solution →If $15$ envelopes cost $Rs.11.25,$ what is the cost of $20$ such envelopes$?$
View full solution →If $\frac{4}{5}$ of a cistern is filled in $1$ minute, how much time will be required to fill the empty cistern$?$
View full solution →If 8kg sugar costs $Rs. 260,$ how much sugar can be bought for $Rs. 877.59?$
View full solution →$1200$ soldiers in a fort had enough food for $28$ days. After $4$ days, some soldiers were transferred to another fort and thus the food lasted for an extra $32$ days. How many soldiers left the fort?
View full solution →Prabhat runs a typing company that processes the manuscripts obtained from publishing companies. There are two processes in this work—typing and typesetting. He owns one team for each of the two processes. He received a manuscript of 3960 pages from a publishing company ABD. He knows that his team of 24 typists can type 264 pages in a day and his team of 6 typesetters can typeset 360 pages in 4 days.
Q.1. How many days will Prabhat's team take to type the manuscript?
(a) 14 days$\quad$(b) 15 days$\quad$(c) 16 days$\quad$(d) 18 days
Q.2. If Prabhat employs 6 more typists in his team, in how many days will he be able to finish the typing work?
(a) $18 \frac{3}{4}$ days$\quad$(b) 15 days$\quad$(c) 12 days$\quad$(d) 10 days
Q.3. In how many days will Prabhat's team of typesetters finish typesetting the work?
(a) 48 days$\quad$ (b) 44 days$\quad$(c) 66 days$\quad$(d) 64 days
Q.4. If typesetting work begins only after the typing work is finished, what is the least number of days Prabhat needs to get the work done with his team of 30 typists and 6 type setters?
(a) 56 days $\quad$(b) 78 days$\quad$(c) 81 days$\quad$(d) 59 days
View full solution →A train covers a distance of $51\ km$ in $45$ minutes. How long will it take to cover $221\ km?$
View full solution →If $22.5$ metres of a uniform iron rod weighs $85.5\ kg,$ what will be the length of $22.8\ kg$ of the same rod$?$
View full solution →Reeta type $40$ words per minute and takes $24$ minutes to type a certain document. Her friend Geeta has a typing speed of $48$ words per minute. In how much time, will she be able to type the same document?
View full solution →A girl can finish a book in $25$ days if she reads $18$ pages of it every day. How many days will she take to finish it, if she reads $15$ pages every day$?$
View full solution →If $48$ men can dig a trench in $14$ days. how long will $28$ men take to dig a similar trench$?$
View full solution →