Compute present worth (PW) and true discount (TD): Find the present worth and the true discount, reckoning 6% per annum simple interest, for Rs. 176 due 20 months from now.

Introduction / Context:Present worth (PW) discounts a future sum A at simple interest: PW = A / (1 + r * t). True discount (TD) is the rebate A − PW that exactly brings A back to today’s value. This exercise uses months converted to years.

Given Data / Assumptions:

• A = 176.
• t = 20 months = 20/12 years = 5/3 years.
• r = 6% p.a. simple.

Concept / Approach:Compute PW with the division formula. Then compute TD = A − PW. Ensure unit conversions are precise to avoid rounding mistakes.

Step-by-Step Solution:PW = 176 / (1 + 0.06 * 5/3) = 176 / (1 + 0.10) = 176 / 1.10 = 160.TD = 176 − 160 = 16.

Verification / Alternative check:Compute TD from its formula: TD = A * (r * t) / (1 + r * t) = 176 * 0.10 / 1.10 = 17.6 / 1.10 = 16, confirming the result.

Why Other Options Are Wrong:

• The other pairs do not satisfy both PW and TD identities simultaneously at r = 6% and t = 20 months.

Common Pitfalls:

• Mistaking 20 months as 2 years instead of 1 year 8 months = 5/3 years.
• Using banker’s discount A * r * t (which would give 17.6) instead of the true-discount value 16.

Final Answer:Rs. 160, Rs. 16