5 Marks Questions

Question 15 Marks

In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and (-2) for every incorrect answer. (and 0 for not attempting any answer). If Yash secured 94 marks in a test, What are the possibilities of his marking correct or incorrect answer?

Answer

Marks scored $=94$
So, minimum correct answers $=\frac{94}{2}=47$
Case I Correct answer $=47$
Marks for correct answers $=2$
Marks for 47 correct answers $=47 \times 2=94$
Marks for incorrect answers $=0$
So, no incorrect answers and 3 unattempted answers.
Case II Correct answers $=48$
Marks for 48 correct answers $=48 \times 2=96$
Marks scored $=94$
Marks obtained for incorrect answer $=94-96=-2$
Marks for one incorrect answer $=-2$
Number of incorrect answers $=(-2) \div(-2)=1$
$\therefore 48$ correct answer, 1 incorrect answer and 1 unattempted answer.
Case III Correct answer $=49$
Marks for 49 correct answers $=49 \times 2=98$
Marks scored $=94$
Marks for incorrect answers $=94-98=-4$
Number of incorrect answers $=(-4) \div (-2)=2$
Thus, number of questions $=49+2=51$
Whereas, total number of questions is 50 .
So, this case is not possible.
Thus, the possible ways are
47 correct answers, 3 unattempted answers
or 48 correct answers, 1 unattempted answer and 1 incorrect answer.

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Question 25 Marks

Observe the following table and complete it.

	Statement	Observation
(i)	7 - 9 = - 2	Result is an integer
(ii)	17 - (- 21) =
(iii)	(- 8) - (-14) = 6	Result is an integer
(iv)	(- 21) - (-10) =
(v)	32 - (- 17) =
(vi)	(- 18) - (- 18) =
(vii)	(- 29) - 0 =

Answer

The complete table is shown as below:

	Statement	Observation
(i)	7 - 9 = - 2	Result is an integer
(ii)	17 - (- 21) = 38	Result is an integer
(iii)	(- 8) - (- 14) = 6	Result is an integer
(iv)	(- 21) - (- 10) = - 11	Result is an integer
(v)	32 - (- 17) = 49	Result is an integer
(vi)	(- 18) - (- 18) = 0	Result is an integer
(vii)	(- 29) - 0 = - 29	Result is an integer

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Question 35 Marks

Observe the following table and complete it.

Statement	Inference
(- 8) $\div$ (- 4) = 2	Result is an integer
(- 4) $\div$ (- 8) = $\frac{- 4}{- 8}$	Result is not an integer
(- 8) $\div$ 3 = $\frac{-8}{3}$
3 $\div$ (- 8) = $\frac{3}{-8}$

Answer

The complete table is shown as below:

Statement	Inference
(- 8) $\div$ (- 4) = 2	Result is an integer
(- 4) $\div$ (- 8) = $\frac{- 4}{- 8}$	Result is not an integer
(- 8) $\div$ 3 = $\frac{-8}{3}$	Result is not an integer
3 $\div$ (- 8) = $\frac{3}{-8}$	Result is not an integer

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Question 45 Marks

Observe the following table and complete it.

Multiplication statement	Corresponding division statements
2 × (- 6) = (- 12)	(- 12) $\div$ (- 6) = 2, (- 12) $\div$ 2 = (- 6)
(- 4) × 5 = (- 20)	(- 20) $\div$ (5) = (- 4), (- 20) $\div$ (- 4) = 5
(- 8) × (- 9) = 72	72 $\div$ __________ = __________ , 72 $\div$ __________ = __________
(- 3) × (- 7) = __________	__________ , $\div$ (-3)= __________ , __________
(- 8) × 4 = __________	__________ , __________
5 × (- 9) = __________	__________ , __________
(- 10) × (- 5) = __________	__________ , __________

Answer

The complete table is shown as below:

Multiplication statement	Corresponding division statements
2 × (- 6) = (- 12)	(- 12) $\div$ (- 6) = 2, (- 12) $\div$ 2 = (- 6)
(- 4) × 5 = (- 20)	(- 20) $\div$ (5) = (- 4), (- 20) $\div$ (- 4) = 5
(- 8) × (- 9) = 72	72 $\div$ (- 8) = (- 9), 72 $\div$ (- 9) = (- 8)
(- 3) × (- 7) = 21	21 $\div$ (- 3) = (- 7), 21 $\div$ (- 7) = (- 3)
(- 8) × 4 = (- 32)	(- 32) $\div$ (- 8) = 4, (- 32) $\div$ 4 = (- 8)
5 × (- 9) = (- 45)	(- 45) $\div$ 5 = (- 9), (- 45) $\div$ (- 9) = 5
(- 10) × (- 5) = 50	50 $\div$ (- 10) = (- 5), 50 $\div$ (- 5) = (- 10)

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Question 55 Marks

Observe the following table and complete it.

Statement 1	Statement 2	Inference
3 × (- 4) = - 12	(- 4) × 3 = - 12	3 × (- 4) = (- 4) × 3
(- 30) × 12 =	12 × (- 30) =
(- 15) × (- 10) = 150	(- 10) × (- 15) = 150
(- 35) × (- 12) =	(- 12) × (- 35) = 420
(- 17) × 0 =
$\quad$$\quad$$\quad$$\quad$=	(- 1) × (- 15) =

Answer

The complete table is shown as below:

Statement 1	Statement 2	Inference
3 × (- 4) = - 12	(- 4) × 3 = - 12	3 × (- 4) = (- 4) × 3
(- 30) × 12 = - 360	12 × (- 30) = 360	(- 30) × 12 = 12 × (- 30)
(- 15) × (- 10) = 150	(- 10) × (- 15) = 150	(- 15) × (- 10) = (- 10) × (- 15)
(- 35) × (- 12) = 420	(- 12) × (- 35) = 420	(- 35) × (- 12) = (- 12) × (- 35)
(- 17) × 0 = 0	0 × (- 17) = 0	(- 17) × 0 = 0 × (- 17)
(- 15) × (- 1) = 15	(- 1) × (- 15) = 15	(- 15) × (- 1) = (- 1) × (- 15)

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Question 65 Marks

Observe the following table and complete it

Statement	Observation
(- 20) × (- 5) = 100	Product is an integer
(- 15) × 17 = - 255	Product is an integer
(- 30) × 12 =
(- 15) × (- 23) =
(- 14) × (- 13) =
12 × (- 30) =

Answer

The complete table is shown as below:

Statement	Observation
(- 20) × (- 5) = 100	Product is an integer
(- 15) × 17 = - 255	Product is an integer
(- 30) × 12 = - 360	Product is an integer
(- 15) × (- 23) = 345	Product is an integer
(- 14) × (- 13) = 182	Product is an integer
12 × (- 30) = - 360	Product is an integer

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Question 75 Marks

Observe the following table and complete it.

	Statement	Observation
(i)	17 + 23 = 40	Result is an integer
(ii)	(- 10) + 3 =
(iii)	(- 75) + 18 =	Result is an integer.
(iv)	19 + (- 25) = - 6
(v)	27 + (- 27) =
(vi)	(- 20) + 0 =
(vii)	(- 35) + (- 10) =

Answer

The complete table is shown as below:

	Statement	Observation
(i)	17 + 23 = 40	Result is an integer
(ii)	(- 10) + 3 = - 7	Result is an integer
(iii)	(- 75) + 18 = - 57	Result is an integer
(iv)	19 + (- 25) = - 6	Result is an integer
(v)	27 + (- 27) = 0	Result is an integer
(vi)	(- 20) + 0 = - 20	Result is an integer
(vii)	(- 35) + (- 10) = - 45	Result is an integer

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Question 85 Marks

An apartment has 30 floors above the ground level each of height 10 m. It also has 2 floors in the basement each of height 5 m. A lift in the apartment moves at a rate of $2 m / s$. If a man starts from 20 m above the ground at 10:00 AM. At what time he will reach at 2 nd floor of basement.

Answer

Height of each floor above the ground level $=10 m$ and height of each floor below the ground level $=5 m$.
$\therefore$ Height below the basement $=5 \times 2=10 m$
Now, since the man starts from 20 m above the grounds and reach the 2nd floor of basement. Then, the total distance to be covered $=20 m+10 m=30 m$
$\because$ Rate of moving of the lift $=2 m / s$
$\therefore$ A man reach at 2 nd floor of basement in $\frac{30 m}{2 m / s }$
$
=150 \sec \left[\because \text { Time }=\frac{\text { Distance }}{\text { Speed }}\right]
$
Since, man starts at $10: 00 AM$ and reach at 2 nd floor of basement in 15 sec .
So, man reaches at 2nd floor of basement at $10: 00: 15 AM$.

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Question 95 Marks

A fruit seller earns a profit of ₹ 6 per bag of mangoes sold and a loss of ₹ 3 per bag of grapes sold.
(i) Fruit seller sells 700 bags of mangoes and 800 bags of grapes. What is his profit or loss?
(ii) If he sold 500 bags of grapes. Then to have neither profit nor loss, how many bags of mangoes, he has to sell?

Answer

(i) Profit earns on mangoes sale = ₹ 6
Loss earns on grapes sale = ₹ 3 (i.e. 3) [here negative sign represents loss)
Now, Profit on sale of 700 mango bags = 700 × ₹ 6
=₹ 4200
Loss on sale of 800 grapes bags = 800 × ₹3
=₹ 2400
Thus, Total Profit = Profit + Loss
= 4200 + (-2400)
= (4200 - 2400)
= 1800
Thus, his total profit is ₹ 1800.
(ii) Seller sold 500 bags of grapes.
$\therefore$Total loss on selling of grapes = 500 × 3 = ₹ 1500
Since, the seller have neither profit nor loss.
$\therefore$Profit earned = loss incurred $\quad \ldots(i)$
Let the number of bags of mangoes to be sold = $x$
Profit earned for selling mangoes's bags= $6x$
Thus, from Eq. (i), we have
$6x$ = 1500
$\Rightarrow$$x$=$\frac{1500}{6}$
$\Rightarrow$$x$ = 250
Thus, seller has to sell 250 bags for no profit and loss.

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Question 105 Marks

In a class test (+6) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question.
(i) Shreya scored 40 marks. If she has got 10 correct answers, how many questions has she attempted incorrectly?
(ii) Shreya scored 24 marks by attempting 8 questions. How many questions has she attempted correctly and how many questions has she attempted incorrectly?

Answer

(i) Marks for each correct answer $=+6$
Marks for each incorrect answer $=-2$
Shreya's marks for correct answer $=10 \times 6$ points
$=60$ points
Since, Shreya's scored $=40$ marks
$\therefore$ Shreya's marks for incorrect answer
$
=40-60=-20
$
$\therefore$ Incorrect answer attempted by Shreya $=\frac{-20}{-2}=10$
Thus, Shreya attempted 10 incorrect answers.
(ii) Let correct answers attempted by Shreya is $x$.
Then, Incorrect answers $=8-x$
Marks scored for correct answers $=6 \times x=6 x$
and marks scored for incorrect answers
$
=(-2) \times(8-x)=-16+2 x
$
Since, Shreya scored $=24$ marks
According to the question,
$6 x+2 x-16=24$
$\begin{array}{ll}\Rightarrow & 8 x=24+16 \\ \Rightarrow & 8 x=40 \Rightarrow x=5\end{array}$
$\therefore$ Shreya attempted 5 correct and 3 incorrect answers.

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Question 115 Marks

Manan deposits ₹ 8000 in a bank account. After some days he withdraw ₹ 4540 and give half of the withdrawal money to his mother. How much total money he had left?

Answer

Deposit amount = ₹ 8000
Withdrawal amount = ₹ 4540
Money given to mother = $\frac{1}{2}$ × withdrawal amount
=$\frac{1}{2}$ × 4540 = 2270
Thus, remaining amount of withdrawal money = 4540 - 2270 = 2270
Thus, the total money left = 2270 + (8000 - 4540)
=2270 + 3460 = 5730
$\therefore$Manan had total ₹ 5730 left now.

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