Exercise: 10-A
Multiple Choice Questions
Q1: If the cost of 40 toys is ₹1024, what is the cost of one dozen such toys?
Total cost of 40 toys = ₹1024
Step 1: Cost of 1 toy = ₹1024 ÷ 40
\[
\text{Cost of 1 toy} = \frac{1024}{40} = 25.6
\]Step 2: One dozen = 12 toys
Cost of 12 toys = ₹25.6 × 12
\[
= 25.6 \times 12 = 307.2
\]Answer: ₹307.20
Q2: If 18 notebooks cost ₹333, how many notebooks can be purchased for ₹425.50?
Cost of 18 notebooks = ₹333
Step 1: Cost of 1 notebook = ₹333 ÷ 18
\[
\text{Cost of 1 notebook} = \frac{333}{18} = 18.5
\]Step 2: Now divide ₹425.50 by the cost of 1 notebook:
\[
\text{Number of notebooks} = \frac{425.50}{18.5} = 23
\]Answer: 23 notebooks
Q3: If 50 pencils can be bought for ₹120, how many pencils can be bought for ₹108?
50 pencils cost ₹120
Step 1: Cost of 1 pencil = ₹120 ÷ 50
\[
\text{Cost of 1 pencil} = \frac{120}{50} = 2.4
\]Step 2: Now divide ₹108 by the cost of 1 pencil:
\[
\text{Number of pencils} = \frac{108}{2.4} = 45
\]Answer: 45 pencils
Q4: If 45 iron rods of the same size weigh 12.6 kg, how much is the weight of 24 such rods?
45 rods weigh 12.6 kg
Step 1: Weight of 1 rod = 12.6 ÷ 45
\[
\text{Weight of 1 rod} = \frac{12.6}{45} = 0.28 \text{ kg}
\]Step 2: Weight of 24 rods = 0.28 × 24 = 6.72 kg
Answer: 6.72 kg
Q5: If a labourer earns ₹784 per week, how much will he earn in 15 days?
Earnings per week = ₹784
Step 1: 1 week = 7 days
So, earnings per day = ₹784 ÷ 7
\[
\text{Daily earning} = \frac{784}{7} = ₹112
\]Step 2: Earnings in 15 days = ₹112 × 15 = ₹1680
Answer: ₹1680
Q6: If a car covers 56.7 km in 4.5 litres of petrol, how many kilometres will it cover in 26 litres of petrol?
56.7 km is covered using 4.5 litres
Step 1: Distance covered per litre = 56.7 ÷ 4.5
\[
\text{Distance per litre} = \frac{56.7}{4.5} = 12.6 \text{ km}
\]Step 2: Distance covered in 26 litres = 12.6 × 26 = 327.6 km
Answer: 327.6 km
Q7: 15 men can do a piece of work in 36 hours. How many men will be required to finish the work in 20 hours?
i. This is an inverse proportion problem
Step 1: Let the required number of men be \( x \)
Since fewer hours means more men are needed, this is inverse variation.
Step 2: Apply the inverse proportion formula:
\[
15 \times 36 = x \times 20 \\
540 = 20x
\]Step 3: Solve for \( x \):
\[
x = \frac{540}{20} = 27
\]Answer: 27 men
Q8: 13 men can weave 117 baskets in a week. How many men will be needed to weave 189 baskets in 3 days?
Step 1: 13 men can weave 117 baskets in 7 days.
1 man can weave 117 baskets in \(7 \times 13\) days.
1 man can weave 1 basket in
\[
\frac{7 \times 13}{117} = \frac{7}{9} \text {days}
\]Step 2: Let the required number of men be \(x\).
\(x\) men can weave 1 basket in \(\frac{7}{x \times 9}\)
Then, \(x\) men can weave 189 basket in
\[
\frac{7 \times 189}{x \times 9} \text {days}
\]
As 189 baskets weaved in 3 days. So,
\[
\frac{7 \times 189}{x \times 9} = 3 \\
7 \times 189 = 27x \\
x = \frac{7 \times 189}{27} = 49
\]Answer: 49 men
Q9: A journey by car takes 48 minutes at 65 kmph. How fast must the car go to finish the journey in 40 minutes?
48 minutes → 65 kmph
We are to find speed for 40 minutes to cover same distance.
Since time decreases, speed must increase ⇒ inverse proportion
Step 1: Let the required speed be \( x \) kmph
Step 2: Apply inverse proportion:
\[
x \times 40 = 65 \times 48 \\
x = \frac{65 \times 48}{40}
\]Step 3: Simplify:
\[
x = \frac{3120}{40} = 78
\]Answer: 78 kmph
Q10: In a zoo, 28 parrots consume 7420 g of nuts in a day. If 8 parrots are sent to another zoo, what quantity of nuts will be required in a day?
28 parrots consume 7420 g/day
New number of parrots = 28 − 8 = 20 parrots
Step 1: Find food consumed by 1 parrot per day:
\[
\text{Nuts per parrot} = \frac{7420}{28} = 265 \text{ g}
\]Step 2: Now multiply by 20 parrots:
\[
\text{Required quantity} = 265 \times 20 = 5300 \text{ g}
\]Answer: 5300 grams
Q11: If 5 men or 7 women can earn ₹700 per day, how much would 7 men and 11 women earn per day?
5 men = ₹700/day and 7 women = ₹700/day
Step 1: Earning per man = ₹700 ÷ 5 = ₹140
\[
\text{1 man’s earning per day} = ₹140
\]Step 2: Earning per woman = ₹700 ÷ 7 = ₹100
\[
\text{1 woman’s earning per day} = ₹100
\]Step 3: Now calculate for 7 men and 11 women:
\[
\text{Earnings of 7 men} = 7 \times 140 = ₹980 \\
\text{Earnings of 11 women} = 11 \times 100 = ₹1100 \\
\text{Total earning per day} = ₹980 + ₹1100 = ₹2080
\]Answer: ₹2080 per day
Q12: If 5 labourers earn ₹9000 in 15 days, how many labourers can earn ₹6720 in 8 days?
Step 1: Total earning = ₹9000
Total labourers = 5
Total days = 15
Step 2: Find the earning of 1 labourer in 1 day:
\[
\text{Earning of 1 labourer in 1 day} = \frac{9000}{5 \times 15} = \frac{9000}{75} = ₹120
\]Step 3: Now, 1 labourer earns ₹120 per day.
Let the required number of labourers be \(x\)
Step 4: Total earning of \(x\) labourers in 8 days = ₹6720
So,
\[
x \times 8 \times 120 = 6720 \\
\Rightarrow 960x = 6720 \\
\Rightarrow x = \frac{6720}{960} = 7
\]Answer: 7 labourers
Q13: A fort had provisions for 450 men for 80 days. After 10 days, 50 more men arrived. How long will the remaining food last at the same rate?
Step 1: Total provision: 450 men for 80 days
After 10 days, the fort has food for 450men for 70 days.
For 450 men, food is sufficient for 70 days.
Step 2: For 1 man food is sufficient for \(70 \times 450\) days.
For 500 (450 + 50) men food is sufficient for
\[
\frac{70 \times 450}{500} \text{ days} = 63 \text { days}
\]Answer: 63 days
Q14: 3 typists working 7 hours a day, type a thesis in 10 days. For how many hours per day should 2 typists work to finish it in 21 days?
Step 1: Total work = 3 typists × 7 hours/day × 10 days
\[
\Rightarrow \text{Total work} = 3 \times 7 \times 10 = 210 \text{ typist-hours}
\]Step 2: Work done by 1 typist in 1 hour = \(\frac{1}{210}\) of the total work
Step 3: Let required hours per day = \(x\)
Now, 2 typists work for \(x\) hours/day for 21 days:
\[
\text{Total work by 2 typists} = 2 \times x \times 21 = 42x
\]This must equal total work = 210
So,
\[
42x = 210 \\
\Rightarrow x = \frac{210}{42} = 5
\]Answer: 5 hours per day
Q15: 7 workers working 6 hours day can build a wall in 12 days. How many days will 3 workers take to build a similar wall, working 8 hours a day?
Step 1: Total work = 7 workers × 6 hours/day × 12 days
\[
= 7 \times 6 \times 12 = 504 \text{ worker-hours}
\]Step 2: Work done by 1 worker in 1 hour = \(\frac{1}{504}\) of the total wall
Step 3: Let required number of days = \(x\)
Now, 3 workers working 8 hours/day for \(x\) days =
\[
3 \times 8 \times x = 24x \text{ worker-hours}
\]This must equal total work = 504
So,
\[
24x = 504 \\
\Rightarrow x = \frac{504}{24} = 21
\]Answer: 21 days
