Sum
The present age of two persons are in the ratio 4: 3. Nine years hence their ages will be in the ratio 23: 18. Find their present ages.
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Solution
Let present ages be 4x and 3x.
`[4 "x" + 9]/[3"x" + 9] = 23 /18`
⇒ 72x + 162 = 69x + 207
⇒ 3x = 45
⇒ x = 15
∴ 3 x = 45
4x = 60
Hence, their present ages are 60 years and 45 years .
Concept: Concept of Ratio
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Chapter 9: Ratio and Proportion - Exercise 9.1
Q 27Q 26Q 28
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Frank ICSE Class 10 Mathematics Part 2
Chapter 9 Ratio and Proportion
Exercise 9.1
| Q 27
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The ages of two persons P and Q are in the ratio 5 : 7. Eight years ago, the ratio of P and Q was 7 : 13. The present ages of P and Q, respectively, are:
- 15 and 21 years
- 20 and 28 years
- 21 and 15 years
- 12 and 13 years
Answer [Detailed Solution Below]
Option 1 : 15 and 21 years
Free
SSC GD Previous Paper 2 [Held On: 13 Feb 2019 Shift 1]_Hindi
100 Questions 100 Marks 90 Mins
Given:
The present age of P∶ The present age of Q = 5 ∶ 7
Eight years ago the age of P ∶ Eight years ago the age of Q = 7 ∶ 13
Calculation:
Let assume that present age of P = 5x
The present age of Q = 7x
Eight years ago
P's age = 5x - 8
Q's age = 7x - 8
According to the question:
\[\frac{5x - 8}{7x - 8} = \frac{7}{13}\]
By cross multiplication:
⇒ 13[5x - 8] = 7[7x - 8]
⇒ 65x - 104 = 49x - 56
⇒ 16x = 48
⇒ x = 3
P's present age = 5x = 5 × 3 = 15 years
Q's present age = 7x = 7 × 3 = 21 years
∴ P's present age is 15 years and Q's present age is 21 years
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Ages of two persons are in the ratio of 5 : 7. 18 years ago, their ages were in the ratio of 8 : 13. Their current ages are:
- 45 and 63 years
- 50 and 70 years
- 40 and 80 years
- 45 and 75 years
Answer [Detailed Solution Below]
Option 2 : 50 and 70 years
Free
Electric charges and coulomb's law [Basic]
10 Questions 10 Marks 10 Mins
Given,
Ratio of ages of two person = 5 : 7
Let the ages of two persons are = 5x, 7x
⇒ [5x – 18]/[7x – 18] = 8/13
⇒ [5x – 18] × 13 = [7x – 18] × 8
⇒ 65x – 234 = 56x – 144
⇒ 9x = 90
⇒ x = 10
Therefore, present age of two person = 5x = 5 × 10 = 50 and 7x = 7 × 10 = 70
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her students are question is the ages of two persons are in the ratio 5 ratio 7 18 years ago their ages were in the ratio of 8 ratio 13 find their present ages right in the question it is given that the ratio of their present ages of two person is 5 ratio 7 right so firstly let the present ages right that the present ages of two persons be 5 x 7 x right as a ratio is 5 ratio 7 so we can say that the present ages of two person are 5% 7x now adding two question it is given that 5 x divided by 7 x 5 with these are the present ages so 18 years ago means 18 we have to subtract 18 from the present ages right so the ratio becomes 8 ratio 13 write the ratio is it a ratio 13 now what we have to do we have to cross multiply the
two fractions of this is equal to 13 into 5 x minus 18 is equal to is equal to 8 into 7 x minus 18 right so 13 into 56565 x minus 13 into 18182 13 so this is equal to 3 and 2824 391345 in 281 this is equal to 8 + 5 is 13 1234 so this is equal to 234 is equal to 18 27 which is equal to 56 x minus 18 in 2818 in 28 is 144 right 18828 is 144 no 65 x 65 x - 56 x is equal to -1 44 + 234 so 65 - 56 is equal to 9 x which is equal to 234 - 144 so this is equal to
13 - 4 is 9 write this is equal to 90 so the value of x is equal to 1999 which is equal to 10 so the value of x series 10 and the present ages are present ages of two persons are 5x and 7 x 5 x is equal to 5 into 10 which is equal to 50 right and 7x mean 7 into 10 which is equal to 70 to the present ages of two persons are 50 and 70