Question
The HCF and LCM of two numbers, A and B, are 9 and 162,
respectively. The difference between these two numbers is 27. Find their sum.Solution
ATQ,
HCF (A, B) = 9
LCM (A, B) = 162
We know that,
HCF (A, B) × LCM (A, B) = A × B
Also, A – B = 27
Or, B = A – 27
ATQ:
A × (A – 27) = 9 × 162
Or, A² – 27A = 1458
Or, A² – 27A – 1458 = 0
Or, A² – 54A + 27A – 1458 = 0
Or, A(A – 54) + 27(A – 54) = 0
Or, (A – 54)(A + 27) = 0
So, A = 54 or A = -27
Since, A cannot be negative, we discard A = -27.
So, A = 54
And, B = 54 – 27 = 27
Therefore, required sum = (54 + 27) = 81
799.99 + 1500.12 ÷ 29.98 × 50.01 = ? × 24.96
- The profit of a business increased by Rs. 300. If the old profit was 30% less than the new profit, then the old profit was:
The combined income of 'Sam' and 'Neil' is Rs. 120,000. If Sam's income were Rs. 35,000 more, it would be 50% more than Neil's original income. Both Sam...
The income of 'Q' surpasses that of 'S' by a suffering 4000%. The expenses of 'Q' and 'S' are in a ratio of 125:12. 'Q' has savings that exceed those of...
Ravi earns 25% more than Rohit, and Rohit spends 75% of what Ravi spends. The ratio of Rohit's savings to Ravi’s savings is 5:7. If Rohit’s expendit...
The monthly incomes of Arjun, Rohan, and Sameer are in the ratio of 7:9:8, while their monthly expenditures are in the ratio of 3:4:5. Arjun earns Rs. 2...
- A allocates his monthly income as follows: 15% for rent, 25% for groceries, and 20% for bills, while saving the remaining amount. If his savings amount to ...
In the last financial year the ratio of the monthly incomes of Viraj and Rohan was m : n and the ratio of their monthly expenditures was p : n. In the c...
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has...
The total monthly salary of Mamta and Rishi is Rs 1,10,000 and the ratio of the expenses of Mamta and Rishi is 7:6 and the ratio of savings of Rishi and...
