Maths Question Paper

1. How much distance will be covered in 5 hrs at a speed of 55 km per hour?

solution:Distance covered in 1 hour = 55 km.

We know, Distance = Speed × Time

Distance covered in 5 hrs = 55 × 5

= 275 km.

Therefore, distance covered in 5 hrs = 275 km.

2. A bus travels at a speed of 45 km/hour. How far will it travel in 36 minutes?

solution:

Speed = 45 km/hour

Time = 36 minutes

= 36/60 Hour (Since we know, 1 hour = 60 minutes)

= 3/5 hour

Distance = speed × time

= 45 × (3/5) km

= (45 × 3)/5 km

= 27 km.

3. How much distance will be covered in 7 hrs at a speed of 62 km per hour?

solution:
Distance covered in 1 hour = 62 km.

We know, Distance = Speed × Time

Distance covered in 7 hrs = 62 × 7

= 434 km.

Therefore, distance covered in 7 hrs = 434 km.

4. Mike drives his car at a speed of 70 km per hour. How much distance will he cover in 3 hours 30 minutes?

solution:Speed of the car = 70 km/hr

Time taken         = 3 hours 30 minutes

= 3 ½ hours.

Distance covered in 1 hour = 70 km

Distance covered in 3 ½ hour = 70 × 3 ½ km

= 70 × 7/2 km

= 245 km.

5. How much distance will be covered in 1 ½ hour at a speed of 32 m per minute?

solution:

[1 ½ hr = (60 + 30) minutes = 90 minutes].

Distance covered in 1 minute = 32 metres.

Distance covered in 90 minutes = 32 × 90 = 2880 m.

We know, 1 m = 1/1000 km.

= 2880/1000 km.

= 2.88 km.

6. Aaron alone can finish a piece of work in 12 days and Brandon alone can do it in 15 days. If both of them work at it together, how much time will they take to finish it?

solution:

Time taken by Aaron to finish the work = 12 days.

Work done by Aaron in 1 day = ¹/₁₂

Time taken by Brandon to finish the work = 15 days.

Work done by Brandon in 1 day = ¹/₁₅

Work done by (Aaron + Brandon) in 1 day = ¹/₁₂ + ¹/₁₅ = ⁹/₆₀ = ³/₂₀

Time taken by (Aaron + Brandon) to finish the work = 206206 days, i.e., 6²/₃ days.

7. A and B together can do a piece of work in 15 days, while B alone can finish it 20 days. In how many days can A alone finish the work?

solution:Time taken by (A + B) to finish the work = 15 days.

Time taken by B alone to finish the work 20 days.

(A + B)’s 1 day’s work = ¹/₁₅

and B’s 1 day’s work = ¹/₂₀

A’s 1 day’s work = {(A + B)’s 1 day’s work} – {B’s 1 day’s work}

= (¹/₁₅ – ¹/₂₀) = (4 – 3)/60 = ¹/₆₀=60 days.

8. A can do a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will B finish the remaining work?

solution:Time taken by A to finish the work = 25 days.

A’s 1 day’s work = ¹/₂₅

Time taken by B to finish the work = 20 days.

B’s 1 day’s work = ¹/₂₀

(A + B)’s 1 day’s work = (¹/₂₅ + ¹/₂₀) = ⁹/₁₀₀

(A + B)’s 5 day’s work (5 × ⁹/₁₀₀) = 4̶5̶/1̶0̶0̶ = ⁹/₂₀

Remaining work (1 – ⁹/₂₀) = ¹¹/₂₀

Now, ¹¹/₂₀ work is done by B in 1 day

Therefore, ¹¹/₂₀ work will be done by B in (11/2̶0̶ × 2̶0̶) days = 11 days.

9. A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. If A, B, C works together, in how many days will they finish the work?

 

solution:Time taken by (A + B) to finish the work = 18 days.

(A + B)’s 1 day’s work = ¹/₁₈

Time taken by (B + C) to finish the work = 24 days.

(B + C)’s 1 day’s work = ¹/₂₄

Time taken by (C + A) to finish the work = 36 days.

(C + A)’s 1 day’s work = ¹/₃₆

Therefore, 2(A + B + C)’s 1 day’s work = (¹/₁₈ + ¹/₂₄ + ¹/₃₆) = (4 + 3 + 2)/72 = 972972 = ¹/₈

⇒ (A + B + C)’s 1 day’s work = (¹/₂ × ¹/₈) = ¹/₁₆

Therefore, A, B, C together can finish the work in 16 days.

10. A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. If A, B, C works together, in how many days will they finish the work? In how many days will each one of them finish it, working alone?

Solution:

Time taken by (A + B) to finish the work = 12 days.

(A + B)’s 1 day’s work = ¹/₁₂

Time taken by (B +C) to finish the work = 15 days.

(B + C)’s 1 day’s work = ¹/₁₅

Time taken by (C + A) to finish the work = 20 days.

(C + A)’s 1 day’s work = ¹/₂₀

Therefore, 2(A + B + C)’s 1 day’s work = (¹/₁₂ + ¹/₁₅ + ¹/₂₀) = 12601260 = ¹/₅

⇒ (A + B + C)’s 1 day’s work = (¹/₂ × ¹/₅) = ¹/₁₀

Therefore, A, B, C together can finish the work in 10 days.

Now, A’s 1 day’s work

= {(A + B + C)’s 1 day’s work} – {(B + C)’s 1 day’s work}

= (¹/₁₀ – ¹/₁₅) = ¹/₃₀

Hence, A alone can finish the work in 30 days.

B’s 1 day’s work

{(A + B + C)’s 1 day’s work} – {(C + A)’s 1 day’s work}

(¹/₁₀ – ¹/₂₀) = ¹/₂₀ Hence, B alone can finish the work in 20 days.

C’s 1 days work

= {(A + B + C)’s 1 day’s work} – {(A + B)’s 1 day’s work}

= (¹/₁₀ – ¹/₁₂) = ¹/₆₀

Hence, C alone can finish the work in 60 days.

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