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EXERCISE 2.4
1. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The
result now obtained is 3 times the same number she thought of. What is the number?
solution:-
Let the number =x
According to Question,
⇒ (x-5/2)8=3x
⇒8x - 5×8/2=3x
⇒8x-20=3x
⇒8x-3x=20
⇒5x=20
⇒x=20/5
⇒x=4
the number is 4 ans
2. A positive number is 5 times another number. If 21 is added to both the numbers,
then one of the new numbers becomes twice the other new number. What are the numbers?
Solution:-
let the another number=x
First number=5x
21 is added to another the number=x+21
21 is added to first the number=5x+21
According to Question,
⇒5x+21=2(x+21)
⇒5x+21=2x +42
⇒5x-2x=42-21
⇒3x=21
⇒x=21/3
⇒x=7
the another number=21
The first number =5 × 7=35
3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?
Solution:- let the ones digit=x
and tens digit = 9-x
digit=10(9-x)+x=90-10x+x=90-9x
interchange the digits=10x+9-x=9x+9
According to Question,
⇒9x+9=90-9x+27
⇒9x+9x=90+27-9
⇒18x=90+18
⇒18x=108
⇒ x=108/18
⇒ x=6
the ones digit=6
tens digit=9-6=3
digit=3×10+6=36
the two-digit number=36 answer
4. One of the two digits of a two digit number is three times the other digit. If you
interchange the digits of this two-digit number and add the resulting number to the
original number, you get 88. What is the original number?
5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five
years from now will be one third of his mother’s present age. What are their
present ages?
6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The
length and breadth of the plot are in the ratio 11:4. At the rate `100 per metre it will
cost the village panchayat ` 75000 to fence the plot. What are the dimensions of
the plot?
7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that
costs him ` 50 per metre and trouser material that costs him ` 90 per metre.For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ` 36,600.How much trouser material did he buy?
8. Half of a herd of deer are grazing in the field and three
fourths of the remaining are playing nearby. The rest 9
are drinking water from the pond. Find the number of
deer in the herd.
9. A grandfather is ten times older than his granddaughter.
He is also 54 years older than her. Find their present ages.
10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s
age. Find their present ages.
