Question

X,Y,W,Z jointly purchased an office space for Rs 84 lakhs. The amount contributed by Y, W and Z put together is three times of X. The amount contributed by X, W and Z put together is 320% of Y. Further, the amount contributed by W is 20% of X, Y and Z put together. What is the contribution of Z?

• A. 32 lakhs
• B. 14 lakhs
• C. 29 lakhs
• D. 42 lakhs

Hint:

Use substitution to reduce the number of variables early in the calculation.

Answer 1

The Correct Option is C

Step 1: Translate each sentence.
Let the contributions be $X, Y, W, Z$ in lakhs. The total is $X + Y + W + Z = 84$. The other three put together being three times $X$ means $Y + W + Z = 3X$.
Step 2: Solve for X.
Substitute $Y + W + Z = 3X$ into the total: $X + 3X = 84$, so $4X = 84$ and $X = 21$.
Step 3: Use the 320 percent clue for Y.
$X + W + Z = 3.2Y$. Since $X + W + Z = 84 - Y$, we get $84 - Y = 3.2Y$, so $84 = 4.2Y$ and $Y = 20$.
Step 4: Apply the W clue.
$W = 0.2(X + Y + Z) = 0.2(84 - W)$, since $X + Y + Z = 84 - W$. Then $W = 16.8 - 0.2W$, so $1.2W = 16.8$ and $W = 14$.
Step 5: Solve for Z.
From the total, $Z = 84 - X - Y - W = 84 - 21 - 20 - 14 = 29$.
Step 6: Sanity check.
Sum is $21 + 20 + 14 + 29 = 84$, correct, and $W = 14$ equals $0.2 \times 70$, consistent. So Z is 29 lakhs, matching option 3.
\[ \boxed{29 \text{ lakhs}} \]