Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
The difference between the present ages of Ayushi and Nidhi is 21 years. Five years ago from now, the sum of their ages was 83 years. If Ayushi is older than Nidhi, find Nidhi's present age (in years).
38
36
31
33
36
Let Nidhi's present age be x, then Ayushi's is x + 21. Five years ago, their ages were x - 5 and x + 16, summing to 83. Solve 2x + 11 = 83 to get 2x = 72, thus x = 36.
Let Nidhi's present age be x, then Ayushi's is x + 21. Five years ago, their ages were x - 5 and x + 16, summing to 83. Solve 2x + 11 = 83 to get 2x = 72, thus x = 36.
Define variables
Let Nidhi's present age be N and Ayushi's present age be A. Given A - N = 21, so A = N + 21.
Apply past age condition
Five years ago, Nidhi was N - 5 and Ayushi was A - 5. The sum of their ages was 83, so (N - 5) + (A - 5) = 83, which simplifies to N + A = 93.
Solve the system
Substitute A = N + 21 into N + A = 93: N + (N + 21) = 93. This gives 2N = 72, meaning N = 36.
A: If Nidhi is 38, Ayushi is 59; 5 years ago sum is 33+54=87 (not 83). C: If Nidhi is 31, Ayushi is 52; 5 years ago sum is 26+47=73 (not 83). D: If Nidhi is 33, Ayushi is 54; 5 years ago sum is 28+49=77 (not 83).
B is correct because solving the linear equation (N-5) + (N+21-5) = 83 yields 2N + 11 = 83, resulting in Nidhi's present age as 36.
In age problems, always subtract the time offset (e.g., 5 years) from both individuals before summing to avoid common calculation errors.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants