Ram is 4 years older than Shyam. After 5 years, the sum of their ages will be 44 years. What is Ram's present age?
Answer and explanation
Correct answer: 19 years
This is a pair of linear equations because the two unknown present ages occur only to the first power. Let Ram’s age be r and Shyam’s age be s. The first statement gives r − s = 4. After five years their ages become r + 5 and s + 5, so their sum is r + s + 10 = 44, or r + s = 34. Adding r − s = 4 and r + s = 34 eliminates s: 2r = 38, hence r = 19. Therefore option C is correct. Checking, Shyam is 15, Ram is 19, and after five years the ages are 24 and 20, whose sum is 44. Options A, B and D do not satisfy both conditions.
Frequently asked questions
What is the correct answer to this question?
19 years
Why is this the correct answer?
This is a pair of linear equations because the two unknown present ages occur only to the first power. Let Ram’s age be r and Shyam’s age be s. The first statement gives r − s = 4. After five years their ages become r + 5 and s + 5, so their sum is r + s + 10 = 44, or r + s = 34. Adding r − s = 4 and r + s = 34 eliminates s: 2r = 38, hence r = 19. Therefore option C is correct. Checking, Shyam is 15, Ram is 19, and after five years the ages are 24 and 20, whose sum is 44. Options A, B and D do not satisfy both conditions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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