Numbers problems
- 1. Two bus tickets from city K to L and three tickets from city K to M cost Rs. 77, but three tickets from city K to L and two tickets from city K to M cost Rs. 73. What are the fares for cities L and M from K ?
Options- A. Rs. 13 and Rs. 17
- B. Rs. 17 and Rs. 19
- C. Rs. 23 and Rs. 17
- D. Rs. 13 and Rs. 19 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: Rs. 13 and Rs. 17
Explanation:
If fares for cities L and M from K are x and y respectively, then
2x + 3y = 77 or 6x + 9y = 231...(1)
3x + 2y = 73 or 6x + 4y = 146...(2)
subtracting 2 from 1, we get
5y = 85
y = Rs. 17 => x = Rs. 13
- 2. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Options- A. 10 & 12
- B. 10 & 18
- C. 12 & -18
- D. -12 & 18 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: -12 & 18
Explanation:
Given, difference of the squares of two numbers is 180.
= k2 - l2 - 180
Also, square of the smaller number is 8 times the larger.
= l2 = 8k
Thus, k2 - 8a - 180 = 0
k2 ? 18k + 10k - 180 = 0
? k(k - 18) + 10(k ? 18) = 0
= (k + 10)(k ? 18) = 0
? k = -10, 18
Thus, the other number is
324 - 180 = l2
? Numbers are 12, 18 or -12, 18.
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