Problems Based on Numbers
Finding the number when decreased after multiplication
Question to obtain the formula: When t times of a number is decreased by d, it gives y, then find the number.
[Here 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield]
Solution
Let the number = n
Thus, according to question,
t × n – d = y
⇒ t n = y + d
∴ n = y + d⁄t
Thus, in such a situation, the required number can be found by using the above given formula
Question (1) If thrice of a number is decreased by 8, it gives 82, then find the number.
Answer
Given,
3 × Number – 8 = 82
Then number = ?
Let the number be a
Thus, as per question,
3 × a – 8 = 82
⇒ 3 a = 82 + 8
⇒ 3 a = 90
∴ a = 90⁄3
⇒ a = 30
Thus, required number = 30 Answer
Alternate Method
This question can be solved using the formula, Number = y + d⁄t
Where 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield
Here in the question,
t = 3, d = 8, y = 82, thus number = ?
By using the formula Number = y + d⁄t
⇒ Number = 82 + 8⁄3
⇒ Number = 90⁄3
⇒ Number = 30
Thus, required number = 30 Answer
Question (2) When four times of a number is decreased by 15, it gives 85. Then, what will be the number?
Answer
Given,
4 × Number – 15 = 85
Then number = ?
Let the number be a
Thus, as per question,
4 × a – 15 = 85
⇒ 4 a = 85 + 15
⇒ 4 a = 100
∴ a = 100⁄4
⇒ a = 25
Thus, required number = 25 Answer
Alternate Method
This question can be solved using the formula, Number = y + d⁄t
Where 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield
Here in the question,
t = 4, d = 15, y = 85, thus number = ?
By using the formula Number = y + d⁄t
⇒ Number = 85 + 15⁄4
⇒ Number = 100⁄4
⇒ Number = 25
Thus, required number = 25 Answer
Question (3) When 5 times of a number is decreased by 20, it gives 130. Find the number.
Answer
Given,
5 × Number – 20 = 130
Then number = ?
Let the number be a
Thus, as per question,
5 × a – 20 = 130
⇒ 5 a = 130 + 20
⇒ 5 a = 150
∴ a = 150⁄5
⇒ a = 30
Thus, required number = 30 Answer
Alternate Method
This question can be solved using the formula, Number = y + d⁄t
Where 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield
Here in the question,
t = 5, d = 20, y = 130, thus number = ?
By using the formula Number = y + d⁄t
⇒ Number = 130 + 20⁄5
⇒ Number = 150⁄5
⇒ Number = 30
Thus, required number = 30 Answer
Question (4) When 15 times of a number is decreased by 120, it gives 2130. Find the number.
Answer
Given,
15 × Number – 120 = 2130
Then number = ?
Let the number be a
Thus, as per question,
15 × a – 120 = 2130
⇒ 15 a = 2130 + 120
⇒ 15 a = 2250
∴ a = 2250⁄15
⇒ a = 150
Thus, required number = 150 Answer
Alternate Method
This question can be solved using the formula, Number = y + d⁄t
Where 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield
Here in the question,
t = 15, d = 120, y = 2130, thus number = ?
By using the formula Number = y + d⁄t
⇒ Number = 2130 + 120⁄15
⇒ Number = 2250⁄15
⇒ Number = 150
Thus, required number = 150 Answer
Question (5) When 20 times of a number is decreased by 135, it gives 1065. Find the number.
Answer
Given,
20 × Number – 135 = 1065
Then number = ?
Let the number be a
Thus, as per question,
20 × a – 135 = 1065
⇒ 20 a = 1065 + 135
⇒ 20 a = 1100
∴ a = 1100⁄20
⇒ a = 55
Thus, required number = 55 Answer
Alternate Method
This question can be solved using the formula, Number = y + d⁄t
Where 't' denotes the times, 'd' denotes the decreased, and 'y' denotes the yield
Here in the question,
t = 20, d = 135, y = 1065, thus number = ?
By using the formula Number = y + d⁄t
⇒ Number = 1065 + 135⁄20
⇒ Number = 1100⁄20
⇒ Number = 55
Thus, required number = 55 Answer
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