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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 this mother’s present age. What are their present ages?
Let Shobo’s age be x years. Therefore, his mother’s age will be 6x years.
According to the given question,
x + 5 = 2x
Transposing x to R.H.S, we obtain
5 = 2x − x
5 = x
6x = 6 × 5 = 30
Therefore, the present ages of Shobo and Shobo’s mother will be 5 years and 30 years respectively.
Amina thinks of a number and subtracts 
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?
Let the number be x.
According to the given question,
= 3x
8x − 20 = 3x
Transposing 3x to L.H.S and −20 to R.H.S, we obtain
8x − 3x = 20
5x = 20
Dividing both sides by 5, we obtain
x = 4
Hence, the number is 4.
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?
Let the numbers be x and 5x. According to the question,
21 + 5x = 2(x + 21)
21 + 5x = 2x + 42
Transposing 2x to L.H.S and 21 to R.H.S, we obtain
5x − 2x = 42 − 21
3x = 21
Dividing both sides by 3, we obtain
x = 7
5x = 5 × 7 = 35
Hence, the numbers are 7 and 35 respectively.
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?
assume the number as "xy" where x and y are first and second digits respectively.
x+y=9 ...............(1)
when interchanging the digits number becomes yx.
yx=xy+27
that is
y*10+x=x*10+y+27
10y+x=10x+y+27
10y-y=10x-x+27
9y=9x+27.................(2)
dividing (2) by 9
y=x+3....................(3)
substituting (3) in (1)
x+y=9
x+x+3=9
2x=9-3
2x=6
x=3
from (3)
y=x+3=3+3=6
number=xy=36
One of the two digits of a two digit number is three times the other digit. If you interchange the digit of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Assume the 2 digit number as xy, where x and y are first and second digits respectively.
x=3y..............(1)
new number after interchanging digits is yx.
xy+yx=88
that means
10x+y+10y+x=88
11x+11y=88
11(x+y)=88
x+y=88/11=8..............(2)
substituting (1) in (2)
3y+y=8
4y=8
y=8/4
y=2
x=3y=3*2=6
original number=xy=62
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 Rs 100 per metre it will cost the village panchayat Rs 75, 000 to fence the plot. What are the dimensions of the plot?
Let the common ratio between the length and breadth of the rectangular plot be x. Hence, the length and breadth of the rectangular plot will be 11x m and 4x m respectively.
Perimeter of the plot = 2(Length + Breadth) 
It is given that the cost of fencing the plot at the rate of Rs 100 per metre is Rs 75, 000.
∴ 100 × Perimeter = 75000
100 × 30x = 75000
3000x = 75000
Dividing both sides by 3000, we obtain
x = 25
Length = 11x m = (11 × 25) m = 275 m
Breadth = 4x m = (4 × 25) m = 100 m
Hence, the dimensions of the plot are 275 m and 100 m respectively.
Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36660. How much trouser material did he buy?
cost of shirt material per unit length=50 rs/m
cost of trouser material per unit length=90 rs/m
For every 2 meters of the trouser material, he buys 3 meters of the shirt material.
ie ratio of shirt to trouser material=3:2
profit of shirt material = 12%
profit of trouser material=10%
total sale =36660
since shirt and trouser length he bought are in the ratio 3:2,
length of shirt material he bought=3k
length of trouser material he bought=2k
cost of shirt material=3k*50=150k
cost of trouser material=2k*90=180k
where k is an integer constant.
selling price=cost price(1+profit/100)
selling price of shirt material=150k*(1+12/100)=150k*(1+0.12)=150*1.12*k=168k
selling price of trouser material=180k*(1+10/100)=180k*(1+0.1)=180*1.1*k=198k
total selling price=168k+198k=366k
366k=36660
k=36660/366~100
trouser material he bought=2k=200 m
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.
fraction of herd grazing=1/2
fraction of herd playing=3/4 * remaining=3/4*1/2=3/8
fraction of herd drinking water=1-1/2-3/8=1/2-3/8=(4-3)/8=1/8
since total of all fractions equals to 1.
let total number of deer in the herd=x
number of deers drinking water=1/8 *x=x/8=9
x=9*8=72
the total number of deer in the herd=72
A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages
present age of grand father=x
present age of grand daughter=y
x=10y...........(1)
x=y+54.............(2)
substituting (1) in (2)
10y=y+54
10y-y=54
9y=54
y=54/9=6
x=10y=10*6=60
present age of grand daughter=6
present age of grand father=60
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.
Let Aman's age=x
son's age=y
x=3y..............(1)
10 years ago aman's age=x-10
10 years ago son's age=y-10
x-10=5(y-10)
x-10=5y-50
x=5y-50+10
x=5y-40............(2)
substituting (1) in (2)
3y=5y-40
5y-3y=40
2y=40
y=40/2=20
x=3y=3*20=60
Aman's age=60
Son's age=20
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