Q.4. The ages of A and B are in the ratio 5:2. Five years ago their ages were in the ratio 3:1. Find their
present ages.
Q.5. The ratio of number of boys and girls in a school is 5:3. If the total number of girls is 912, find the
number of boys.
Q.6. The ratio of monthly income to savings of a family is 15:2. If the savings be Rs 1600. Find the
income and expenditure.
Q.7. A bag contains Rs. 1880 in the form of currency notes of Rs 20, Rs 50 and Rs 100 with ratio 6:3:2.
Find the number of notes of each denomination.
Answers
Answer:
Step-by-step explanation:
A:B = 5:3
This can also be expressed as a fraction, when the given values are reduced (for example, 21/15):
A/B = 5/3
You can solve for either A or B here, but let’s solve for A
First, multiply both sides by B:
A = (5b)/3
In the second equation, A and B both increase by 6:
(A+6)/(B+6) = 7:5
recall that A = 5b/3
So substitute for A in the first equation:
((5b/3)+6)/(B+6) = 7:5
Multiply both sides by (b+6) to get rid of the denominator
((5b/3)+6) = (7(B+6)/5
Now, expand the parentheses on the right side:
((5b/3)+6)=(7b+42)/5
Drop the parentheses on the left side
(5b/3)+6 = (7b+42)/5
Multiply both sides by 15 to get rid of both denominators
15(5b/3)+15*6 = 15(7b+42)/5
(75b/3)+15*6 = 3(7b+42)
Use FOIL on the right side:
(75b/3)+15*6 = 21b+126
25b + 90 = 21b + 126
Subtract 21b from both sides, then subtract 90 from both sides:
4b = 36
Divide by 4:
b = 9
Now go back to the very first equation and pop in 9 for b:
A:B = 5:3
b = 9
A/9 = 5/3
Multiply both sides by 9:
A = 45/3
A = 15
Now go back to the second equation from the question and substitute and see if it fits:
(A+6)/(B+6) = 7/5
(15+6)/(9+6)=7/5
21/15 = 7/5
7/5 = 7/5
So the ages are 15 and 9.
Q5 5x+3x = 912
8x = 912
x = 912/8
x = 114
5x (no. of boys) = 5×114
= 570
Hence, number of boys in the school is 570.
.
Q6 Income=Savings + expenditure.
Ratio=11:2.
So let the monthly income be 11x and saving be 2x.
2x=2500
x=1250.
11x=11*1250
=13750.
Expenditure=Income- savings
=13750-2500
=11250
Therefore,Income= Rs.13750 and expenditure= Rs.11250
Q7 Let the number of Rs. 10 notes =2x
Let the number of Rs. 20 notes =3x
Value of Rs. 10 notes =2x×10=Rs.20x
Value of Rs. 20 notes =3x×20=Rs.60x
Total money in the bag =Rs.1600
So,
20x+60x=1600
80x=1600
x=
80
1600
x=20
The number of Rs. 10 notes =2x=40
the number of Rs. 20 notes =3x=60
Total number of notes =40+60=100
HOPE IT IS HELPFULL