3 Marks Question

Question 13 Marks

A man bought some pencils for $Rs. 30$ and some pens for $Rs. 90$. The next day, he again bought some pencils for $Rs. 25.$ Then he sold all the pencils for $Rs. 20$ and the pens for $Rs. 70$. What was his net gain or loss?

Answer

Total cost price = Price of pencils $+$ Price of pens $= 30 + 90 + 25 = Rs. 145$
Total amount sold = Price of pen $+$ Price of pencils $= 20 + 70 = Rs. 90$
Selling price $–$ Cost price $= 90 – 145 = -55$
The negative sign implies loss Hence, his net loss was $Rs. 55.$

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Question 23 Marks

Complete the following multiplication table:

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$-3$
$-2$
$-1$
$0$
$1$
$2$
$3$

Answer

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$-3$	$+9$	$+6$	$+3$	$0$	$-3$	$-6$	$-9$
$-2$	$+6$	$+4$	$+2$	$0$	$-2$	$-4$	$-6$
$-1$	$+3$	$+2$	$+1$	$0$	$-1$	$-2$	$-3$
$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
$1$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$2$	$-6$	$-4$	$-2$	$0$	$2$	$4$	$6$
$3$	$-9$	$-6$	$-3$	$0$	$3$	$6$	$9$

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Question 33 Marks

Verify the following: $(-13) \times [(-6) + (-19)] = (-13) \times (-6) + (-13) \times (-19)$

Answer

$L.H.S. (-13) \times [(-6) + (-19)] $
$= (-13) \times [-6 - 19] $
$= (-13) \times (-25) $
$= 325 R.H.S. (-13) \times (-6) + (-13) \times (-19) $
$= 78 + 247 $
$= 325 L.H.S. $
$= R.H.S.$ (Proved)

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Question 43 Marks

Verify the following: $18 \times [9 + (-7)] = 18 \times 9 + 18 \times (-7)$

Answer

$L.H.S. 18 \times [9 + (-7)] = 18 \times 2 = 36 R.H.S. 18 \times 9 + 18 \times (-7) = 162 + (-126) = 36 So, L.H.S. = R.H.S$. (Proved)

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Question 53 Marks

A car travelled $60\ km$ to the north of Patna and then $90\ km$ to the south from there. How far from Patna was the car finally?

Answer

Let the distance covered in the direction of north be positive and that in the direction of south be negative. Distance travelled to the north of Patna $= 60\ km$ Distance travelled to the south of Patna $= -90\ km$ Total distance travelled by the car = 60 + (-90) = -30\ km The car was $30\ km$ south of Patna.

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Question 63 Marks

Subtract the sum of $-250$ and $138$ from the sum of $136$ and $-272.$

Answer

Sum of 138 and -250:$138 + (-250)$
$= 138 - 250$
$= -112$
Sum of 136 and -272:
$= 136 + (-272)$
$= 136 - 272$
$= -136$
Subtracting the sum of -250 and 138 from the sum of 136 and -272:
$-136 - (-112)$
$= -136 + 112$
$= -24$

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