156 is divided into two parts such that seven times the first part and five times the second part are in the ratio 5 : 2. Find the first part.
Explanation:
Let the numbers be x and 156 – x
7x5(156-x)=52
⇒ 14x = 25 × 156 - 25x
⇒ 39x = 25 × 156
⇒ x = 25 × 4 = 100
∴ The first part is 100.
Hence, 100.
Alternately,
Let the numbers be a and b.
Hence, a + b = 156, and
7a5b=52
⇒ ab=2514
⇒ a = 25/39 × 156 = 100.
Hence, option (c).
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