Problem 1 :
Mr. David's salary is hiked by $225 this month and he is paid $3250. What was his last month salary?
Problem 2 :
There are two numbers such that the sum of the smaller number and two times the bigger number is equal to 13. If the smaller number is 3, find the bigger number.
Problem 3 :
Lily thought a number. She took half of the number and multiplied it by 3 and divided the result by 15. Then, she subtracted 7 from the result and got the final answer -2. What number did she think?
Problem 4 :
Dividing the sum of three consecutive numbers results 4 results 3. Find the smallest of the three consecutive numbers.
Problem 5 :
If a number of which the half is greater than 1/5th of the number by 15, find the number.
Problem 6 :
Three persons A, B and C together have $51. B has $4 less than A. C has got $5 less than A. Find the money that A, B and C have.
Problem 7 :
The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. Find the age of the youngest boy.
Problem 8 :
The ratio of the number of boys to the number of girls in a school of 720 students is 3 : 5. If 18 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of the number of boys to the number of girls may change to 2 : 3.
1. Answer :
Let x be the Mr. David's salary last month.
Given : Mr. David's salary is increased by $225 and he is paid $3250 this month.
x + 225 = 3250
Subtract 225 from both sides.
x = 3025
Mr. David's last month salary was $3025.
2. Answer :
Let x be the bigger number.
Given : Sum of the smaller number and two times the bigger number is equal to 13 and the smaller number is 3.
3 + 2x = 13
Subtract 3 from both sides.
2x = 10
Divide both sides by 2.
x = 5
The bigger number is 5.
3. Answer :
Let x be the number Lily thought.
Given : Lily took half of the number and multiplied it by 3 and divided the result by 15. Further, she subtracted 7 from the result and got the final answer -2
[3(ˣ⁄₂) ÷ 3] - 7 = -2
Add 7 to both sides.
3(ˣ⁄₂) ÷ 3 = 5
3(ˣ⁄₂) ÷ ³⁄₁ = 5
Change the division to multiplication by taking reciprocal of ³⁄₁.
3(ˣ⁄₂) x ⅓ = 5
Multiply both sides by 3.
3(ˣ⁄₂) = 15
Divide both sides by 3.
ˣ⁄₂ = 5
Multiply both sides by 2.
x = 10
Lily thought the number 10.
4. Answer :
Let x be the smallest of the three consecutive numbers.
Then, the remaining two numbers are
(x + 1) and (x + 2)
Given : When sum of the three consecutive numbers is divided by 4, the answer is 3.
(x + x + 1 + x + 2) ÷ 4 = 4
(3x + 3) ÷ 4 = 4
⁽³ˣ ⁺ ³⁾⁄₄ = 4
Multiply both sides by 4.
3x + 3 = 12
Subtract 3 from both sides.
3x = 9
Divide both sides by 3.
x = 3
The smallest of the three consecutive number is 3.
5. Answer :
Let x be the required number.
Half of the number = ˣ⁄₂.
⅕ the of the number :
= ⅕ ⋅ x
= ˣ⁄₅
Given : Half of a number is greater than 1/5th of the number by 15.
ˣ⁄₂ = ˣ⁄₅ + 15
L.C.M of (2 , 5) is 10. So, multiply both sides of the above equation by 10 to get rid of the denominators 2 and 5..
10(ˣ⁄₂) = 10(ˣ⁄₅ + 15)
5x = 10(ˣ⁄₅) + 10(15)
5x = 2x + 150
Subtract 2x from both sides.
3x = 150
Divide both sides by 3.
x = 50
Hence, the required number is 50.
6. Answer :
Let x be the money that A had.
A = x
B has $4 less than A ----> B = x - 4.
C has got $5 less than A ----> C = x - 5.
Given : A, B and C together have $51.
A + B + C = 51
x + (x - 4) + (x - 5) = 51
x + x - 4 + x - 5 = 51
3x - 9 = 51
Add 9 to both sides.
3x = 60
Divide both sides by 3.
x = 20
x - 4 = 20 - 4 = 16
x - 5 = 20 - 5 = 15
Hence, A, B and C have $20, $16 and $15 respectively.
7. Answer :
From the ratio 3 : 5 : 7, the ages of three boys are
3x, 5x and 7x
Given : Average age of the three boys is 25 years.
⁽³ˣ ⁺ ⁵ˣ ⁺ ⁷ˣ⁾⁄₃ = 25
¹⁵ˣ⁄₃ = 25
Multiply both sides by 3.
5x = 25
Divide both sides by 5.
x = 5
Then, ages of the three boys are
3x = 3 ⋅ 5 = 15
5x = 5 ⋅ 5 = 25
7x = 7 ⋅ 5 = 35
Hence, the age of the youngest boy is 15 years.
8. Answer :
Sum of the terms in the given ratio 3 : 5 is
= 3 + 5
= 8
So, number of boys in the school is
= ⅜ of total students
= ⅜ ⋅ 720
= 270
Number of girls in the school is
= ⅝ of total students
= ⅝ ⋅ 720
= 450
Let x be the number of new boys admitted in the school.
Given : Number of new girls admitted is 18.
After the above new admissions,
number of boys in the school = 270 + x
number of girls in the school = 450 + 18 = 468
Given : The ratio after the new admission is 2 : 3.
(270 + x) : 468 = 2 : 3
⁽²⁷⁰ ⁺ ˣ⁾⁄₄₆₈ = ⅔
Do cross multiplication.
3 ⋅ (270 + x) = 2 ⋅ 468
810 + 3x = 936
Subtract 810 from both sides.
3x = 126
Divide both sides by 3.
x = 42
Hence the number of new boys admitted in the school is 42.
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