UGCNET Questions

Simple interest is computed using the formula I = (P × R × T) ÷ 100. Substituting the given values P = 5,000, R = 8% and T = 3 years gives I = (5,000 × 8 × 3) ÷ 100. The product 5,000 × 8 × 3 is 120,000, and dividing by 100 yields 1,200. Therefore, the simple interest over 3 years is ₹1,200.

Option A:
Option A, ₹1,000, corresponds to a lower effective rate or shorter time period and does not match the product in the interest formula. It underestimates the interest earned.

Option B:
Option B, ₹1,100, is not an exact multiple of P × R × T ÷ 100 and therefore cannot result from correctly applying the formula.

Option C:
Option C aligns perfectly with the given parameters. It reflects three years of interest at 8% per annum on ₹5,000 and matches both the multiplication and division steps.

Option D:
Option D, ₹1,300, overstates the interest and could only be obtained by using a higher rate or an additional year, neither of which is specified.

Let the total number of people be represented as 100%. If 20% like neither tea nor coffee, then 80% like at least one of the two beverages. By the inclusion–exclusion principle, the percentage who like at least one is the sum of tea-likers and coffee-likers minus those who like both. Thus, 80 = 70 + 40 − (both). Solving this gives (both) = 70 + 40 − 80 = 30%.

Option A:
Option A, 20%, equals the proportion who like neither, not those who like both, and so confuses the outside region with the intersection.

Option B:
Option B calculates the intersection using inclusion–exclusion and ensures that the total does not exceed 100%. It matches the only value that makes the percentages internally consistent.

Option C:
Option C, 40%, would give 70 + 40 − 40 = 70% liking at least one, which contradicts the information that 20% like neither and thus only 80% like at least one.

Option D:
Option D, 50%, creates an even larger overlap and leads to a sum exceeding the allowed total, making the data inconsistent.