Bihar School Examination Board (BSEB) Class 8 Mathematics: Direct and Inverse Proportions

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Direct and Inverse Proportions

   1.

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

   1. (A)

      30

   2. (B)

      20

   3. (C)

      28

   4. (D)

      24

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   Answer: (D)

   24

   This is an inverse proportion problem. If $W_1$ workers take $T_1$ hours and $W_2$ workers take $T_2$ hours, then $W_1 T_1 = W_2 T_2$. So, $15 \times 48 = W_2 \times 30$, which gives $W_2 = (15 \times 48) / 30 = 24$ workers.

   Direct and Inverse Proportions · Medium

2. 2.

   A car travels 165 km in 3 hours. How long will it take to travel 440 km at the same speed?

   1. (A)

      7 hours

   2. (B)

      9 hours

   3. (C)

      8 hours

   4. (D)

      6 hours

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   Answer: (C)

   8 hours

   This is a direct proportion problem. If distance $D_1$ is covered in time $T_1$ and distance $D_2$ in time $T_2$, then $D_1/T_1 = D_2/T_2$. So, $165/3 = 440/T_2$, which gives $T_2 = (440 \times 3) / 165 = 8$ hours.

   Direct and Inverse Proportions · Medium

3. 3.

   If $x$ and $y$ are in inverse proportion, and $x = 12$ when $y = 8$, what is the value of $y$ when $x = 16$?

   1. (A)

      4

   2. (B)

      12

   3. (C)

      10

   4. (D)

      6

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   Answer: (D)

   6

   For inverse proportion, the product $xy$ is constant. So, $12 \times 8 = 16 \times y$, which means $96 = 16y$. Therefore, $y = 96/16 = 6$.

   Direct and Inverse Proportions · Easy

4. 4.

   A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long will the remaining provisions last for the remaining men?

   1. (A)

      84 days

   2. (B)

      70 days

   3. (C)

      90 days

   4. (D)

      105 days

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   Answer: (C)

   90 days

   Initially, there were provisions for $300 \times 90 = 27000$ man-days. After 20 days, $300 \times 20 = 6000$ man-days were consumed. Remaining man-days are $27000 - 6000 = 21000$. The remaining men are $300 - 50 = 250$. So, the provisions will last for $21000 / 250 = 84$ days.

   Direct and Inverse Proportions · Hard

5. 5.

   The cost of 5 kg of wheat is Rs 90. What will be the cost of 8 kg of wheat?

   1. (A)

      Rs 120

   2. (B)

      Rs 135

   3. (C)

      Rs 150

   4. (D)

      Rs 144

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   Answer: (D)

   Rs 144

   This is a direct proportion problem. The cost per kg is $90/5 = 18$ Rs/kg. So, the cost of 8 kg of wheat will be $8 \times 18 = 144$ Rs.

   Direct and Inverse Proportions · Easy

— End of the paper · updated 14 October 2026 —