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1.

A rectangle and a square are of equal area. If the length and the perimeter of a rectangle are 25 cm and 58 cm respectively, then find the perimeter and area of the square?

Answer» Let thelength of rectangle =l=25cm
Breath=bcm
Side of square=acm
Area of square=are of rectangle
`a^2=lb-(1)`
Perimeter=2(l+b)=58
l+b=29
b=4 cm
Area of square`(a^2)=lb=25*4=100 cm^2`
`a=10 cm`
Perimeter of square=4a
`4*10=10 cm`.
Discussion
2.

Sunita purchased 5 kg 75g of fruits and 3 kg 485 gm of vegetables and put them in a bag. If this bag with these contents weighs 9 kg, find the weight of the empty bag.

Answer» `1000gram=1kilogram`
`1gram=1/1000 kilogram`
`=0.001gram`
Fruits`=5kilogram+75gram`
`=5kilogram+0.075kilogram`
`=5.075kg`
vegetables= `3kilogram + 485gram`
`=(3+0.485)kilogram`
`=3.485kilogram`
Fruits+vegetables`=5.075+3.485`kilogram
`=8.560kilogram`
(Fruits+vegetables+bag)=`9kilogram`
weight of the empty bag= `9kilogram - (8.560)`
`=0.440kilogram`
`or 440 grams`
Discussion
3.

Merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?

Answer» total money initially with the merchant =`78,592`
cost of 40 radioset`= 40*1200`
`= 48000` rs
money left = `78592- 48000`
`= 30592`rs
answer
Discussion
4.

Write the remainder obtained when 1! + 2! + 3! + ..... + 200! is divided by 14

Answer» Here, the given expression is,
`1!+2!+3!+...+200!`
`1! = 1`
`2! = 2**1=2`
`3! = 3**2**1 = 6`
`4! = 4**3**2**1 = 24`
`5! = 5**4**3**2**1 = 120`
`6! = 6**5**4**3**2**1 = 720`
`7! = 7**6**5**4**3**2**1 = 5040`
So, `7!` is divisible by `14`.
Now, `8! = 8**7!`
So, `8!` will also be divisible by `14`.Similarly, every term greater than `7!` in the given expression will be divisible by `14`.
So, sum of the terms that are not divisible by `14` is,
`1!+2!+3!+4!+5!+6! = 1+2+6+24+120+720 = 873`
`:.` Remainder of `873` when divided by `14` will be `5` which is the required answer.
Discussion
5.

Sunny cuts off `3/8` of a paper strip. What portion of the strip is left?

Answer» Sunny cuts off `3/8` part of a strip.
`:.` Remaining strip `= 1-3/8 = 5/8`
Discussion
6.

40 seconds + 28 seconds is equal to:

Answer» 1 min=60 sec
40+28=68 sec
=60sec+8sec
=1min8sec.
Discussion
7.

The product of two numbers is 19200 and their HCF is 40. Find their LCM

Answer» Here, we will use the formula,
Product of two numbers = HCF of numbers `xx` LCM of numbers
Here, product of numbers ` = 19200`
HCF of numbers ` = 40`
`:. 40 xx LCM = 19200`
`=>LCM = 19200/40 = 480`
So, LCM of given numbers is `480`.
Discussion
8.

Find the sum of successor of n and predecessor of n

Answer» Predecessor of `n= n -1`
Successor of `n = n+1`
`:.` Sum of successor and predecessor of `n= n-1+n+1 = 2n`
Discussion
9.

`[40-:{19-3(6-bar(4-1))}]`

Answer» Using bod-mass.`[40div{19-3(6-3)}]`
`[40div{19-3*3}]`
`[40div{10}]`
`40div10`
`4`.
Discussion
10.

You know that `1/7`=0.`bar(142857)` can you predict what the decimal expansion of `2/7, 3/7,4/7 , 5/7, 6/7 ` are without actually doing the long division.

Answer» `1/7=0.overline142857`
`2/7=2*1/7=2*0.overline142857=0.overline285714`
`3/7=0.overline428571`
`4/7=0.overline571428`
`5/7=0.overline714285`
`6/7=0.overline857142`.
Discussion
11.

In quadrilateral ACBD, AC= AD and AB bisects L A . Show that triangle ABC is congruent to triangle ADB. What can you say about BC and BD?

Answer» `/_CAB=/_DAB`
`/_ABC and /_ABD`
`AC=AD`
`/_CAB=/_OAB`
AB side is common
So, by SAS rule(side-angle-side)
`/_ABC cong /_ABD`
`/_ABC cong /_ABD`
`/_CAB=/_DAB`
if two triangle are congrent.
Side corresponding to same angle. They are equal
`/_CAB=/_DAB`
therefore BC=BD.
Discussion
12.

Determine the H.C.F of the numbers given by prime factorisation method(3) 48 and 64

Answer» `48 = 2*2*2*2*3 = 2^4*3`
`64 = 2*2*2*2*2*2 = 2^6`
HCF will be the common factors of the two numbers.
`:.` HCF of `48` and `64 = 2^4 = 16.`
Discussion
13.

Estimate each of the following using general rule:(a) 730 + 998     (b) 796 – 314     (c) 12,904 +2,888      (d)   28,292 – 21,496Make ten more such examples of addition, subtraction and estimation of their outcome.

Answer» (a) 730+998``
`730->700`
`998-> 1000`
`700+1000 = 1700`
(b) `796-314`
`796-> 800`
`314-> 300`
`800-300= 500`
(c) `12904 + 2888`
`12904-> 13000`
`2888 -> 3000`
`13000+3000 = 16000`
(d) `28292-21496`
`28292->28000`
`21496-> 21000`
`28000-21000= 7000`
examples are :
1) `12-6`
`12-> 10, 6->6`
`10-6=4`
2) `56-31`
`56-> 100, 31->30`
`100-30=70`
3)`78+42`
`78-> 100 , 42->40`
`100+40=140`
4) `740+878`
`740-> 700, 878-> 900`
`700+900= 1600`
5) `370+288`
`370-> 400, 288->300`
`400+300= 700`
6) `572- 223`
`572->600`
`223 - > 200`
`600-200= 400`
7) `411-191`
`411-> 400 , 191-> 200`
`400-200= 200`
8) `1904+ 2718`
`1904-> 2000, 2718-> 3000`
`2000+3000 = 5000`
9) `3708- 2242`
`3708-> 4000`
`2242-> 2000`
`4000-2000= 2000`
10) `19 -1`
`19-> 20 , 1->0`
`20-0= 20`
answer
Discussion
14.

Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate(by rounding off to nearest tens) :(a)   439 + 334 + 4,317          (b)    1,08,734 – 47,599       (c)    8325 – 491(d)   4,89,348 – 48,365Make four more such examples.

Answer» (a) `439+334+4317`
When rounding off to nearest hundreds,
`400+300+4300 = 5000`
When rounding off to nearest tens,
`440+330+4320 = 5090`

(b) `108734 - 47599`
When rounding off to nearest hundreds,
`108700 - 47600 = 61400`
When rounding off to nearest tens,
`108730 - 47600 = 61430`

(c) `8325 - 491`
When rounding off to nearest hundreds,
`8300 - 500 = 7800`
When rounding off to nearest tens,
`8330 - 490 = 7840`

(d) `489348 - 48365`
When rounding off to nearest hundreds,
`489300 - 48400 = 440900`
When rounding off to nearest tens,
`489350 - 48370 = 440980`
Discussion