myhelper: RD Sharma solution class 7 chapter 10 Unitary Method Objective Type Questions

RD Sharma solution class 7 chapter 10 Unitary Method Objective Type Questions

Objective Type Questions

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Question 1:

Mark the correct alternative in the following question:

What distance (in m) will a train cover in 1 minute travelling at 72 km/hr?

(a) 120 (b) 1200 (c) 1400 (d) 720

Answer 1:

As, the speed of the train = 72 km / hr \Rightarrow The distance covered in 1 hr (60 \min) = 72 km ∴ The distance covered in 1 \min = \frac{72}{60} km = \frac{6}{5} km = \frac{6}{5} \times 1000 m = 6 \times 200 = 1200 m

Hence, the correct alternative is option (b).

Question 2:

Mark the correct alternative in the following question:

If the cost of 15 mangoes is ₹180, then what is the cost of 25 mangoes?

(a) ₹220 (b) ₹360 (c) ₹200 (d) ₹300

Answer 2:

As, the cost of 15 mangoes = ₹180

⇒ The cost of 1 mango =

\frac{180}{15}

= ₹12

So, the cost of 25 mangoes = 25 × 12 = ₹300

Hence, the correct alternative is option (d).

Question 3:

Mark the correct alternative in the following question:

If the cost of 25 pencils is ₹75, then the cost of 75 pencils is

(a) ₹225 (b) ₹150 (c) ₹180 (d) ₹100

Answer 3:

As, the cost of 25 pencils = ₹75

⇒ The cost of 1 pencil =

\frac{75}{25}

= ₹3

So, the cost of 75 pencils = 3 × 75 = ₹225

Hence, the correct alternative is option (a).

Question 4:

Mark the correct alternative in the following question:

The cost of 30 mangoes is less then cost of 40 mangoes by ₹50. Find the cost of 50 mangoes in (₹)

(a) 400 (b) 300 (c) 250 (d) 350

Answer 4:

As, the cost of 30 mangoes is less than the cost of 40 mangoes by = ₹50

⇒ The cost of 10 mangoes = ₹50

⇒ The cost of 1 mango =

\frac{50}{10}

= ₹5

So, the cost of 50 mangoes = 5 × 50 = ₹250

Hence, the correct alternative is option (c).

Question 5:

Mark the correct alternative in the following question:

45 cows can graze a field in 12 days. How many cows will graze the same field in 9 days?

(a) 60 cows (b)

38 \frac{3}{4}

cows (c) 54 cows (d) 45 cows

Answer 5:

As, the number of cows that can graze the field in 12 days = 45

⇒ The number of cows that can graze the field in 1 days = 45 × 12 = 540

So, the number of cows that can graze the field in 9 days =

\frac{540}{9}

= 60 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.

Question 6:

Mark the correct alternative in the following question:

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 (b) 15 minutes (c) 12 minutes (d) 10 minutes

Answer 6:

As, the time taken to fill

\frac{4}{5}

of the water tank = 1 hr = 60 min

⇒ The time taken to fill the water tank = 60 ×

\frac{5}{4}

= 15 × 5 = 75 min

So, the time required to fill the rest of the water tank = 75 − 60 = 15 min

Hence, the correct alternative is option (b).

Question 7:

Mark the correct alternative in the following question:

A worker makes a toy every

\frac{2}{3}

hour. If he works for

7 \frac{1}{3}

hours, then how many toys will he make?

(a) 11 (b) 16 (c) 18 (d) 22

Answer 7:

As, the number of toys made by the worker in

\frac{2}{3}

hour = 1

⇒ 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} (\frac{22}{3})

hours =

\frac{3}{2} \times \frac{22}{3}

= 11

Hence, the correct alternative is option (a).

Question 8:

Mark the correct alternative in the following question:

6 dozen eggs are bought for ₹108. How much will 108 eggs cost?

(a) ₹171 (b) ₹162 (c) ₹153 (d) ₹180

Answer 8:

As, the cost of 6 dozen eggs (6 × 12 = 72 eggs) = ₹108

⇒ The cost of 1 egg =

\frac{108}{72} = \frac{3}{2}

So, the cost of 108 eggs =

\frac{3}{2} \times 108 = 3 \times 54

= ₹162

Hence, the correct alternative is option (b).

Question 9:

Mark the correct alternative in the following question:

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 (b) 32 days (c) 36 days (d) 25 days

Answer 9:

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 × 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.

Question 10:

Mark the correct alternative in the following question:

If 21 cows eat as much as 15 buffaloes, then how many cows will eat as much as 35 buffaloes?

(a) 45 (b) 49 (c) 56 (d) 54

Answer 10:

As, the number of cows that eat as much as 15 buffaloes = 21

⇒ 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} \times 35

= 7 × 7 = 49

Hence, the correct alternative is option (b).

Question 11:

Mark the correct alternative in the following question:

If 6 bowls cost ₹90, then the cost of 10 such bowls is

(a) ₹125 (b) ₹175 (c) ₹150 (d) ₹120

Answer 11:

As, the cost of 6 bowls = ₹90

⇒ The cost of 1 bowl =

\frac{90}{6}

= ₹15

So, the cost of 10 bowls = 15 × 10 = ₹150

Hence, the correct alternative is option (c).

Question 12:

Mark the correct alternative in the following question:

A car can go 150 km with 25 litres of petrol. How for can it go with 30 litres of petrol?

(a) 180 km (b) 150 km (c) 210 km (d) 160 km

Answer 12:

As, the distance travelled by the car with 25 litres of petrol = 150 km

⇒ The distance travelled by the car with 1 litre of petrol =

\frac{150}{25}

= 6 km

So, the distance travelled by the car with 30 litres of petrol = 6 × 30 = 180 km

Hence, the correct alternative is option (a).

Question 13:

Mark the correct alternative in the following question:

If the cost of 12 books is ₹144, then the cost of 18 books is

(a) ₹206 (b) ₹216 (c) ₹198 (d) ₹180

Answer 13:

As, the cost of 12 books = ₹144

⇒ The cost of 1 book =

\frac{144}{12}

= ₹12

So, the cost of 18 books = 12 × 18 = ₹216

Hence, the correct alternative is option (b).

Question 14:

Mark the correct alternative in the following question:

If a person travels 150 km in 5 hours, then the time taken by him to travel 180 km is

(a) 3 hours (b) 4 hours (c) 8 hours (d) 6 hours

Answer 14:

As, the time taken by the person to travel 150 km = 5 hours

⇒ The time taken by him to travel 1 km =

\frac{5}{150} = \frac{1}{30}

hours

So, the time taken by him to travel 180 km =

\frac{1}{30} \times 180

= 6 hours

Hence, the correct alternative is option (d).

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Question 15:

Mark the correct alternative in the following question:

If a person travels 60 km in 4 hours in a car, then the speed of the car is

(a) 12 km/hr (b) 15 km/hr (c) 20 km/hr (d) 24 km/hr

Answer 15:

As, the distance travelled by the car in 4 hours = 60 km

⇒ The distance travelled by the car in 1 hour = $\frac{60}{4}$ = 15 km

So, the speed of the car is 15 km/hr.

Hence, the correct alternative is option (b).