The salaries of A and B together amounts to 26000. If they spend 75% and 60% of their respective salaries and their saving are equal, then their respective salaries should be
Answers
Step-by-step explanation:
Let the ratio of salary of A, B, C be x, y, z respectively. Sum of salary x+y+z = 72000 Rs
Spending 80% , 85% , 75%
Savings 20x:15y:25z => 4x:3y:5z = 8:9:20
=> x =2 , y=3, z=4
Therefore salary ratio A:B:C = x:y:z = 2:3:4
Salary of A = 72000 x 2/(2+3+4)
= 72000x2/9= 16000 Rs = answer
Verification:
Salary of A = Rs 16000 (already calculated)
Salary of B = Rs 24000 <= (72000×3/9)
Salary of C = Rs 320000 <=(72000×4/9)
Total salary = 16000+24000+32000=72000 => true.
Savings of A:B:C => (100-80)×16000/100 : (100-85)×24000/100: (100-75)×32000/100= 3200:3600:8000
=> 8:9:20 ---- true.
Concept
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
Given
salaries of A and B amounts to 26000.
A spend 75% of it's salary and B spends 60% of it's salary.
A and B save equally.
Find
the respective salaries of A and B.
Solution
let the salary of A be a and B be b.
given, a ₊ b = 26000 ....eq(1)
A spend 75% of it's salary = 25/100 a
B spends 60% of it's salary = 40/100 b
⇒ both savings are equal
25/100 a = 40/100 b
25 a = 40 b
5 a = 8 b
a = 8b/5
substitute a value in eq (1)
8b/5 ₊ b = 26000
8b ₊ 5b = 5 × 26000
13b = 130000
b = 10,000
substitute b value in eq 1
a ₊ b = 26000
a ₊c = 26000
a = 26000 ₋ 10,000
a = 16,000
hence we get the salaries of A and B as 16,000 and 10,000 respectively.
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