Please answer me fast (word problems)
a) The digits of a two digit number differ by 3. If the digits are interchanged and the
two numbers are added, their sum is 77. Find the numbers.
b) There are 90 multiple choice questions in a test. Suppose you get 2 marks for every
correct answer and for every question you leave unattempted or answer wrongly,
one mark is deducted from your total score of correct answers. If you get 60 marks
in the test, then how many questions did you answer correctly?
c) Rs 561 are divided among A, B and C such that A’s share is Rs 120 more than B’s
share and Rs 120 less than C’s. What is the share of B?
d) The grandfather is ten times elder than his granddaughter. He is also 54 years elder than her. Find their present ages.
e) A steamer goes downstream and coves the distance between two ports in 5 hours
while it covers the same distance upstream in 6 hours. If the speed of the stream is
1km/hr, find the speed of the steamer in still water.
f) A lady has a total of Rs 850 in coins of denomination Rs 1, Rs 2 and Rs 5. The number
of Rs 2 coins is 5 times the number of Rs 5 coins. The total number of coins is 400.
How many coins of each denomination are with her?
Answers
Answer:
a) Let the digit at units place be x
Let the digit at tens place be x + 3
10(x + 3) + x
When digits interchanged, the number becomes 10x + x + 3
According to the question,
10(x + 3) + x + 10x + x + 3 = 77
10x + 30 + 12x + 3 = 77
22x + 33 = 77
22x = 77 - 33
22x = 44
x = \frac{44}{22}2244
x = 2
∴ The number = 10(x + 3) + x = 10 * 5 + 3 + 5 = 50 + 3 + 5 = 53 + 5 = 58
∴ The number is 58
b)Let the number of questions answered correctly by ′x′
∴ The number of questions answered correctly=90−x
Total Marks obtained=60
Marks obtained for correct answer=22
Marks deducted for wrong answer=−1(90−2)=x−90
∴2x+2−90=60
⇒3x=150
⇒x=3150
⇒x=50
Therefore the number of question answered correctly is 50
c) Let A's share be x
Let B's share be x-120
Let C's share be x+120
Total money=561
x+(x-120)+(x+120)
3x =561
x=187
then B's share is = 187-120= rs 67
d) The grandfather and his granddaughter's present age. Granddaughter's age is 10 times lesser than the grandfather and the grandfather's age is 54 more than his granddaughter. Thus, the present ages of grandfather and his granddaughter are 60 years and 6 years respectively.
e) Given
Speed of the stream in still water =1km/h
Let speed of the streamer =xkm/h
Speed downstream =(x+1)km/h
Speed upstream =(x−1)km/h
According to the given condition,
(x+1)×5=(x−1)×6
5x+5=6x−6
x=11
Hence , Speed of streamer in still water is 11km/h and
Distance between two ports =(11+1)×5=60km/h
f) Let number of Rs5 coins be x
Number of Rs 2 coins =3× Number of 5 Rs coins =3x
Number of Re1 coins =160−(x+3x)
=160−4x
Amount of Rs5 coins =5×x=5x
Amount of Rs2 coins =2×3x=Rs6x
Amount of Re1 coins =(160−4×x)
=160−4x
As per the question, Total amount =Rs300
160−4x+5x+6x=300
7x=300−160
x=7140
x=20
Number of Re 1 coins =160−4x
=160−4×20
=80
Number of Rs2 coins =3x=3×20=60
Number of Rs5 coins =x=20
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