Question : The costs of the two watches were in the ratio 16 : 23. The cost of the first watch increased by 10% and that of the second by Rs. 477. Now the costs of two watches are in a ratio of 11 : 20. The price of the second watch (in Rs.) in the beginning was:
Option 1: 932
Option 2: 1219
Option 3: 1696
Option 4: 848
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Correct Answer: 1219
Solution :
Let the initial costs of the first and second watches be $16x$ and $23x$ respectively.
The cost of the first watch increased by 10%. The new cost,
$=1.10 \times 16x = 17.6x$
The cost of the second watch increased by Rs. 477. The new cost,
$=23x + 477$
Now, the costs of the two watches are in the ratio 11 : 20.
⇒ $\frac{17.6x}{23x + 477} = \frac{11}{20}$
⇒ $\frac{88x}{5(23x + 477)} = \frac{11}{20}$
⇒ $1760x-1265x=26235$
⇒ $495x=26235$
⇒ $x=53$
The price of the second watch at the beginning = 53 × 23 = Rs. 1219
Hence, the correct answer is 1219.
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