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Maths 1 Marks Question

Unitary Method · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 14 questions.

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14 questions · 13 auto-graded MCQ + 1 self-marked written.

MCQ 11 Mark
What distance (in m) will a train cover in $1$ minute travelling at $72\frac{\text{km}}{\text{h}}$?
  • A
    $120$
  • ✓
    $1200$
  • C
    $1400$
  • D
    $720$
Answer
Correct option: B.
$1200$
As, the speed of the train $=72\frac{\text{km}}{\text{hr}}$
$\Rightarrow $ The distance covered in $1$ hour ($60$ min) $=72\text{km}$
$\therefore$ The distance covered in $1$ minute $=\frac{72}{60}\text{km}$
$=\frac{6}{5}\text{km}$
$=\frac{6}{5}\times1000\text{m}$
$=6\times200\text{m}$
$=1200\text{m}$
Hence, the correct alternative option $(b)$.
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MCQ 21 Mark
If a person travels $150km$ in $5$ hours, then the time taken by him to travel $180km$ is:
  • A
    $3$ hours
  • B
    $4$ hours
  • C
    $8$ hours
  • ✓
    $6$ hours
Answer
Correct option: D.
$6$ hours
As, the time taken by the person to travel $150km = 5$ hours
$\Rightarrow $ The time taken by him to travel $1km$ $=\frac{5}{150}=\frac{1}{30}\text{ hours}$
So, the time taken by him to travel $180km$ $=\frac{1}{30}\times180\text{ hours}=6 \text{ hours}$
Hence, the correct alternative is option $(d)$.
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MCQ 31 Mark
The cost of $30$ mangoes is less then cost of $40$ mangoes by $Rs. 50$. Find the cost of $50$ mangoes in (Rs.)
  • A
    $400$
  • B
    $300$
  • ✓
    $250$
  • D
    $350$
Answer
Correct option: C.
$250$
As, the cost of $30$ mangoes is less than the cost of $40$ mangoes by $Rs. 50$
$\Rightarrow $ The cost of $10$ mangoes $= Rs. 50$
$\Rightarrow $ The cost of $1$ mango $=\frac{50}{10}=\text{Rs. }5$
So, the cost of $50$ mangoes $= 5 \times 50 = Rs. 250$
Hence, the correct alternative option $(c)$.
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MCQ 41 Mark
If $\frac{4}{5}$ of a water tank is filled in $1$ hour, then how much time will be required to fill the rest of it?
  • A
    $20$ minutes
  • ✓
    $15$ minutes
  • C
    $12$ minutes
  • D
    $10$ minutes
Answer
Correct option: B.
$15$ minutes
As, the time taken to fill $\frac{4}{5}$ of the water tank $= 1$hr $= 60$min
$\Rightarrow $ The time taken to fill the water tank $=60\times\frac{5}{4}=15\times5=75\text{min}$
So, the time required to fill the rest of the water tank $= 75 - 60 = 15$min
Hence, the correct alternative is option $(b)$.
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MCQ 51 Mark
If $6$ bowls cost $Rs. 90$, then the cost of $10$ such bowls is:
  • A
    $Rs. 125$
  • B
    $Rs. 175$
  • ✓
    $Rs. 150$
  • D
    $Rs. 120$
Answer
Correct option: C.
$Rs. 150$
As, the cost of $6$ bowls $= Rs. 90$
$\Rightarrow $ The cost of $1$ bowl $=\frac{90}{6}=\text{Rs. }15$
So, the cost of $10$ bowls $= 15 \times 10 = Rs. 150$
Hence, the correct alternative is option $(c)$.
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MCQ 61 Mark
$8$ men can finish a piece of work in $40$ days. If $2$ more men join them, then the work will be computed in:
  • A
    $30$ days
  • ✓
    $32$ days
  • C
    $36$ days
  • D
    $25$ days
Answer
Correct option: B.
$32$ days
As, the number of days computed by $8$ men to finish the piece of work $= 40$ days
$\Rightarrow $ The number of days computed by $1$ man to finish the piece of work $= 40 \times 8 = 320$ days
So, the number of days computed by $10$ men to finish the piece of work $= \frac{320}{10}=32$ days
Hence, the correct alternative is option $(b)$.
Note: This is the case of inverse variation.
More men needs less time to finish the same work.
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MCQ 71 Mark
If the cost of $15$ mangoes is $Rs. 180$, then what is the cost of $25$ mangoes?
  • A
    $220$
  • B
    $360$
  • C
    $200$
  • ✓
    $300$
Answer
Correct option: D.
$300$
As, the cost of $15$ mangoes $= Rs. 180$
$⇒$ The cost of $1$ mango $=\frac{180}{15}=\text{Rs. }12$
So, the cost of $25$ mangoes $= 25 \times 12 = Rs. 300$
Hence, the correct alternative option $(d)$.
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MCQ 81 Mark
$6$ 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
Correct option: B.
$Rs. 162$
As, the cost of $6$ dozen eggs $(6 \times 12 = 72$ eggs$)$ $= Rs. 108$
$\Rightarrow $ The cost of $1$ egg $=\frac{108}{72}=\frac{3}{2}$
So, the cost of $108$ eggs $=\frac{3}{2}\times108=3\times54=\text{Rs. }162$
Hence, the correct alternative is option $(b)$.
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MCQ 91 Mark
A worker makes a toy every $\frac{2}{3}\text{hr}$. If he works for $7\frac{1}{3}\text{hr}$, then how many toys will he make?
  • ✓
    $11$
  • B
    $16$
  • C
    $18$
  • D
    $22$
Answer
Correct option: A.
$11$

As, the number of toys made by the worker in $\frac{2}{3}\text{hr}=1$
$\Rightarrow $ The number of toys made by him in $1$ hour $=1\times\frac{3}{2}=\frac{3}{2}$
So, the number of toys made by the worker in $7\frac{1}{3}\text{hr }\Big(\frac{22}{3}\Big)\text{hr}=\frac{3}{2}\times\frac{22}{3}=11$
Hence, the correct alternative is option $(a)$.

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MCQ 101 Mark
If the cost of $12$ books is $Rs. 144$, then the cost of $18$ books is:
  • A
    $Rs. 206$
  • ✓
    $Rs. 216$
  • C
    $Rs. 198$
  • D
    $Rs. 180$
Answer
Correct option: B.
$Rs. 216$

As, the cost of $12$ books $= Rs. 144$
$\Rightarrow $ The cost of $1$ book $\frac{144}{12}=\text{Rs. }12$
So, the cost of $18$ books $= 12 \times 18 = Rs. 216$
Hence, the correct alternative is option $(b)$.

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MCQ 111 Mark
If $21$ cows eat as much as $15$ buffaloes, then how many cows will eat as much as $35$ buffaloes?
  • A
    $45$
  • ✓
    $49$
  • C
    $56$
  • D
    $54$
Answer
Correct option: B.
$49$
As, the number of cows that eat as much as $15$ buffaloes $= 21$
$\Rightarrow $ The number of cows that eat as much as $1$ buffalo $=\frac{21}{15}=\frac{7}{5}$
So, the number of cows that eat as much as $35$ buffaloes $=\frac{7}{5}\times35=7\times7=49$
Hence, the correct alternative is option $(b)$.
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MCQ 121 Mark
A car can go $150km$ with $25$ litres of petrol. How for can it go with $30$ litres of petrol?
  • ✓
    $180$
  • B
    $150$
  • C
    $210$
  • D
    $160$
Answer
Correct option: A.
$180$
As, the distance travelled by the car with $25$ litres of petrol $= 150km$
$\Rightarrow $ The distance travelled by the car with $1$ litre of petrol $\frac{150}{25}=6\text{km}$
So, the distance travelled by the car with $30$ litres of petrol $= 6 \times 30 = 180km$
Hence, the correct alternative is option $(a)$.
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MCQ 131 Mark
If the cost of $25$ pencils is $Rs. 75$, then the cost of $75$ pencils is:
  • A
    $ 225$
  • B
    $150$
  • C
    $ 180$
  • D
    $ 100$
Answer
As, the cost of $25$ pencils $= Rs. 75$
$\Rightarrow $ The cost of $1$ pencil $=\frac{75}{25}=\text{Rs. }3$
So, the cost of $75$ pencils $= 3 \times 75 = Rs. 225$
Hence, the correct alternative option $(a)$.
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MCQ 141 Mark
$45$ cows can graze a field in $12$ days. How many cows will graze the same field in $9$ days?
  • ✓
    $60$ cows
  • B
    $38\frac{3}{4}\text{ cows}$
  • C
    $54$ cows
  • D
    $45$ cows
Answer
Correct option: A.
$60$ cows

As, the number of cows that can graze the field in $12$ days $= 45$
$\Rightarrow $ The number of cows that can graze the field in $1$ days $= 45 \times 12 = 540$
So, the number of cows that can graze the field in $9$ days $=\frac{540}{9}=60\text{ cows}$
Hence, the correct alternative is option $(a)$.
Note: This is a situation of inverse variation. More the number of cows, the faster will they graze the field.
The options given in the book are incorrect. The same has been corrected here.

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